AGC002

link

A

求\(a,a+1,\dots ,b\)的积是正，负还是0

若\(a\le 0\le b\)也就是区间包含0 那就是0

若\(0\lt a\)则是正

否则若\(b-a\)是偶数则为负否则为正。

B

n个盒子，每个盒子里有一个球，其中1号盒子中是红球，其它的是白球。

m次操作，每次从\(x_i\)盒子中随机拿出一个球放入\(y_i\)盒子，求最后有几个盒子中可能有红球。

每次操作时，如果\(x_i\)盒子中可能有红球，那\(y_i\)盒子就也有可能。

如果\(x_i\)盒子没球了，当然就不可能了。

C

有\(n\)根绳子，第\(i\)根长度为\(a_i\)，第\(i\)根的尾端和第\(i+1\)根的首端用一个结连在了一起，练成了一根长绳。

你需要把这\(n-1\)个绳结解开。你每次可以选一根长度\(\ge L\)的绳子，解开其中一个绳结，然后就会断成两根。

求一个合法顺序或判断不合法。

显然最后一次解的一定是两根绳子连成的一根绳子。

首先判断是否存在连续两根绳子长度和\(\ge L\)。

找到它们中间的结，然后它之前从前往后，它之后从后往前一个一个解开，最后解开这个结。

D

有一个\(n\)点\(m\)边的无向联通图。

有\(Q\)对兄弟，每对兄弟一个在\(x_i\)一个在\(y_i\)，它们在图上闲逛游走，其中每条边，每个点都可以经过多次。他们希望有\(z_i\)个点至少被其中一个人经过一次，在此基础上，他们希望走过的边编号最大值最小。求这个最大值的最小值。

Kruskal重构树+二分答案即可做到\(O(n\log^2 n)\)，当然也可以用整体二分做到\(O(n\log n)\)，如果你并查集写了按秩合并和路径压缩，如果只有一个还要多个\(\log\)。

E

桌子上有\(n\)堆糖果。第\(i\)堆有\(a_i\)个。Snuke和Ciel在玩一个游戏：两个人轮流操作，每次可以选择把数量最多的一堆糖全吃掉或者把每一堆糖吃掉一个。吃掉最后一个糖的人输，问先手必胜还是后手必胜。

定义\((x,y)\)表示操作\(1\)进行了\(x\)次，操作\(2\)进行了\(y\)次。

将\(a\)从大到小排序得到\(a_0\dots a_{n-1}\)，则若\(y\ge a_x\),\((x,y)\)是必胜态。

（前\(x\)堆已经1操作吃掉了，第\(x+1\)堆也没有那么多，所以后面的也全被吃掉了。然后这个局面交到你手里的时候，游戏已经结束了

并且，若\((x+1,y+1)\)局面存在（就是这个局面游戏还没结束）\((x,y)\)和\((x+1,y+1)\)必胜必败的情况是一样的：

1. 如果\((x+1,y+1)\)后手必胜，则不管先手使\(x+1\)还是\(y+1\)，后手都能操作把\((x+1,y+1)\)给先手，所以\((x,y)\)后手必胜。

2. \((x+1,y+1)\)先手必胜。由于必胜必败态的定义，显然\((x+2,y+1)\)和\((x+1,y+2 )\)先手必败。那么不管怎么动，根据1对面都必败。

所以只需要找到最大的\(x\)使得\((x,x)\)局面存在，然后判断\((x,x)\)的状态即可。

显然\((x,x)\)只能不断向上，或者不断向右，如果存在一个方向使得走到先手必败状态需要奇数步，那么先手必胜。

F

有\(nk\)个球，一共\(n\)个颜色(\(1\dots n\))，每个\(k\)个。把这\(nk\)个球排成一行，然后把每种颜色第一个球变成0色。求得到\(nk\)个球本质不同的颜色序列有多少个。

设\(f(x,y)\)表示考虑了\(x\)个0色球和\(y\)个其它的颜色的方案数，显然\(x\ge y\)，答案为\(f(n,n)\)。

转移？

1. 加入一个0色球。\(f(x-1,y)\)
2. 加入一个非0色球。然后后面的位置中要选出(k-2)个来放这个颜色球，然后这个颜色其它球和它们的位置就可以无视掉了。加入这个非0色球后，剩余的位置还有\((n-x)+(n-y+1)(k-1)-1\)，\(\binom{(n-x)+(n-y+1)(k-1)-1}{k-1}f(x,y-1)\)

然后就能得到转移方程。注意上面是没考虑颜色顺序的，所以还要乘上\(n!\)。

注意\(k=1\)要特判

Code

A

/*
Author: CNYALI_LK
LANG: C++
PROG: a.cpp
Mail: cnyalilk@vip.qq.com
*/
#include<bits/stdc++.h>
#define debug(...) fprintf(stderr,__VA_ARGS__)
#define DEBUG printf("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#define Debug debug("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#define all(x) x.begin(),x.end()
#define x first
#define y second
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
const signed inf=0x3f3f3f3f;
const double eps=1e-8;
const double pi=acos(-1.0);
template<class T>int chkmin(T &a,T b){return a>b?a=b,1:0;}
template<class T>int chkmax(T &a,T b){return a<b?a=b,1:0;}
template<class T>T sqr(T a){return a*a;}
template<class T>T mmin(T a,T b){return a<b?a:b;}
template<class T>T mmax(T a,T b){return a>b?a:b;}
template<class T>T aabs(T a){return a<0?-a:a;}
template<class T>int dcmp(T a,T b){return a>b;}
template<int *a>int cmp_a(int x,int y){return a[x]<a[y];}
#define min mmin
#define max mmax
#define abs aabs
namespace io {
	const int SIZE = (1 << 21) + 1;
	char ibuf[SIZE], *iS, *iT, obuf[SIZE], *oS = obuf, *oT = oS + SIZE - 1, c, qu[55]; int f, qr;
	// getchar
	#define gc() (iS == iT ? (iT = (iS = ibuf) + fread (ibuf, 1, SIZE, stdin), (iS == iT ? EOF : *iS ++)) : *iS ++)
	// print the remaining part
	inline void flush () {
		fwrite (obuf, 1, oS - obuf, stdout);
		oS = obuf;
	}
	// putchar
	inline void putc (char x) {
		*oS ++ = x;
		if (oS == oT) flush ();
	}
	// input a signed integer
	inline void read (signed &x) {
		for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;
		for (x = 0; c <= '9' && c >= '0'; c = gc()) x = x * 10 + (c & 15); x *= f;
	}

	inline void read (long long &x) {
		for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;
		for (x = 0; c <= '9' && c >= '0'; c = gc()) x = x * 10 + (c & 15); x *= f;
	}
	inline void read (char &x) {
		x=gc();
	}
	inline void read(char *x){
		while((*x=gc())=='\n' || *x==' '||*x=='\r');
		while(!(*x=='\n'||*x==' '||*x=='\r'))*(++x)=gc();
	}
	template<typename A,typename ...B>
	inline void read(A &x,B &...y){
		read(x);read(y...);
	}
	// print a signed integer
	inline void write (signed x) {
		if (!x) putc ('0'); if (x < 0) putc ('-'), x = -x;
		while (x) qu[++ qr] = x % 10 + '0',  x /= 10;
		while (qr) putc (qu[qr --]);
	}

	inline void write (long long x) {
		if (!x) putc ('0'); if (x < 0) putc ('-'), x = -x;
		while (x) qu[++ qr] = x % 10 + '0',  x /= 10;
		while (qr) putc (qu[qr --]);
	}
	inline void write (char x) {
		putc(x);
	}
	inline void write(const char *x){
		while(*x){putc(*x);++x;}
	}
	inline void write(char *x){
		while(*x){putc(*x);++x;}
	}
	template<typename A,typename ...B>
	inline void write(A x,B ...y){
		write(x);write(y...);
	}
	//no need to call flush at the end manually!
	struct Flusher_ {~Flusher_(){flush();}}io_flusher_;
}
using io :: read;
using io :: putc;
using io :: write;
int main(){
#ifdef cnyali_lk
	freopen("a.in","r",stdin);
	freopen("a.out","w",stdout);
#endif
	int a,b;
	read(a,b);
	write(a<=0?(0<=b?"Zero\n":(a-b&1?"Positive\n":"Negative\n")):"Positive\n");
	return 0;
}

B

/*
Author: CNYALI_LK
LANG: C++
PROG: b.cpp
Mail: cnyalilk@vip.qq.com
*/
#include<bits/stdc++.h>
#define debug(...) fprintf(stderr,__VA_ARGS__)
#define DEBUG printf("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#define Debug debug("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#define all(x) x.begin(),x.end()
#define x first
#define y second
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
const signed inf=0x3f3f3f3f;
const double eps=1e-8;
const double pi=acos(-1.0);
template<class T>int chkmin(T &a,T b){return a>b?a=b,1:0;}
template<class T>int chkmax(T &a,T b){return a<b?a=b,1:0;}
template<class T>T sqr(T a){return a*a;}
template<class T>T mmin(T a,T b){return a<b?a:b;}
template<class T>T mmax(T a,T b){return a>b?a:b;}
template<class T>T aabs(T a){return a<0?-a:a;}
template<class T>int dcmp(T a,T b){return a>b;}
template<int *a>int cmp_a(int x,int y){return a[x]<a[y];}
#define min mmin
#define max mmax
#define abs aabs
namespace io {
	const int SIZE = (1 << 21) + 1;
	char ibuf[SIZE], *iS, *iT, obuf[SIZE], *oS = obuf, *oT = oS + SIZE - 1, c, qu[55]; int f, qr;
	// getchar
	#define gc() (iS == iT ? (iT = (iS = ibuf) + fread (ibuf, 1, SIZE, stdin), (iS == iT ? EOF : *iS ++)) : *iS ++)
	// print the remaining part
	inline void flush () {
		fwrite (obuf, 1, oS - obuf, stdout);
		oS = obuf;
	}
	// putchar
	inline void putc (char x) {
		*oS ++ = x;
		if (oS == oT) flush ();
	}
	// input a signed integer
	inline void read (signed &x) {
		for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;
		for (x = 0; c <= '9' && c >= '0'; c = gc()) x = x * 10 + (c & 15); x *= f;
	}

	inline void read (long long &x) {
		for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;
		for (x = 0; c <= '9' && c >= '0'; c = gc()) x = x * 10 + (c & 15); x *= f;
	}
	inline void read (char &x) {
		x=gc();
	}
	inline void read(char *x){
		while((*x=gc())=='\n' || *x==' '||*x=='\r');
		while(!(*x=='\n'||*x==' '||*x=='\r'))*(++x)=gc();
	}
	template<typename A,typename ...B>
	inline void read(A &x,B &...y){
		read(x);read(y...);
	}
	// print a signed integer
	inline void write (signed x) {
		if (!x) putc ('0'); if (x < 0) putc ('-'), x = -x;
		while (x) qu[++ qr] = x % 10 + '0',  x /= 10;
		while (qr) putc (qu[qr --]);
	}

	inline void write (long long x) {
		if (!x) putc ('0'); if (x < 0) putc ('-'), x = -x;
		while (x) qu[++ qr] = x % 10 + '0',  x /= 10;
		while (qr) putc (qu[qr --]);
	}
	inline void write (char x) {
		putc(x);
	}
	inline void write(const char *x){
		while(*x){putc(*x);++x;}
	}
	inline void write(char *x){
		while(*x){putc(*x);++x;}
	}
	template<typename A,typename ...B>
	inline void write(A x,B ...y){
		write(x);write(y...);
	}
	//no need to call flush at the end manually!
	struct Flusher_ {~Flusher_(){flush();}}io_flusher_;
}
using io :: read;
using io :: putc;
using io :: write;
int maybe[100005],cnt[100005];
int main(){
#ifdef cnyali_lk
	freopen("b.in","r",stdin);
	freopen("b.out","w",stdout);
#endif
	int n,m,u,v;
	read(n,m);
	for(int i=1;i<=n;++i)cnt[i]=1;
	maybe[1]=1;
	for(;m;--m){
		read(u,v);
		++cnt[v];
		if(maybe[u]){maybe[v]=1;}
		if(!(--cnt[u])){maybe[u]=0;}
	}
	int sum=0;
	for(int i=1;i<=n;++i)if(maybe[i])++sum;
	printf("%d\n",sum);
	return 0;
}

C

/*
Author: CNYALI_LK
LANG: C++
PROG: c.cpp
Mail: cnyalilk@vip.qq.com
*/
#include<bits/stdc++.h>
#define debug(...) fprintf(stderr,__VA_ARGS__)
#define DEBUG printf("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#define Debug debug("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#define all(x) x.begin(),x.end()
#define x first
#define y second
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
const signed inf=0x3f3f3f3f;
const double eps=1e-8;
const double pi=acos(-1.0);
template<class T>int chkmin(T &a,T b){return a>b?a=b,1:0;}
template<class T>int chkmax(T &a,T b){return a<b?a=b,1:0;}
template<class T>T sqr(T a){return a*a;}
template<class T>T mmin(T a,T b){return a<b?a:b;}
template<class T>T mmax(T a,T b){return a>b?a:b;}
template<class T>T aabs(T a){return a<0?-a:a;}
template<class T>int dcmp(T a,T b){return a>b;}
template<int *a>int cmp_a(int x,int y){return a[x]<a[y];}
#define min mmin
#define max mmax
#define abs aabs
namespace io {
	const int SIZE = (1 << 21) + 1;
	char ibuf[SIZE], *iS, *iT, obuf[SIZE], *oS = obuf, *oT = oS + SIZE - 1, c, qu[55]; int f, qr;
	// getchar
	#define gc() (iS == iT ? (iT = (iS = ibuf) + fread (ibuf, 1, SIZE, stdin), (iS == iT ? EOF : *iS ++)) : *iS ++)
	// print the remaining part
	inline void flush () {
		fwrite (obuf, 1, oS - obuf, stdout);
		oS = obuf;
	}
	// putchar
	inline void putc (char x) {
		*oS ++ = x;
		if (oS == oT) flush ();
	}
	// input a signed integer
	inline void read (signed &x) {
		for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;
		for (x = 0; c <= '9' && c >= '0'; c = gc()) x = x * 10 + (c & 15); x *= f;
	}

	inline void read (long long &x) {
		for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;
		for (x = 0; c <= '9' && c >= '0'; c = gc()) x = x * 10 + (c & 15); x *= f;
	}
	inline void read (char &x) {
		x=gc();
	}
	inline void read(char *x){
		while((*x=gc())=='\n' || *x==' '||*x=='\r');
		while(!(*x=='\n'||*x==' '||*x=='\r'))*(++x)=gc();
	}
	template<typename A,typename ...B>
	inline void read(A &x,B &...y){
		read(x);read(y...);
	}
	// print a signed integer
	inline void write (signed x) {
		if (!x) putc ('0'); if (x < 0) putc ('-'), x = -x;
		while (x) qu[++ qr] = x % 10 + '0',  x /= 10;
		while (qr) putc (qu[qr --]);
	}

	inline void write (long long x) {
		if (!x) putc ('0'); if (x < 0) putc ('-'), x = -x;
		while (x) qu[++ qr] = x % 10 + '0',  x /= 10;
		while (qr) putc (qu[qr --]);
	}
	inline void write (char x) {
		putc(x);
	}
	inline void write(const char *x){
		while(*x){putc(*x);++x;}
	}
	inline void write(char *x){
		while(*x){putc(*x);++x;}
	}
	template<typename A,typename ...B>
	inline void write(A x,B ...y){
		write(x);write(y...);
	}
	//no need to call flush at the end manually!
	struct Flusher_ {~Flusher_(){flush();}}io_flusher_;
}
using io :: read;
using io :: putc;
using io :: write;
int a[100005];
void putans(int n,int x){
	for(int i=1;i<x;++i)write(i,'\n');
	for(;--n>x;)write(n,'\n');
	write(x,'\n');
}
int main(){
#ifdef cnyali_lk
	freopen("c.in","r",stdin);
	freopen("c.out","w",stdout);
#endif
	int n,L;
	read(n,L);
	for(int i=1;i<=n;++i)read(a[i]);
	for(int i=1;i<n;++i)if(a[i]+a[i+1]>=L){write("Possible\n");putans(n,i);return 0;}
	write("Impossible\n");
	return 0;
}

D

/*
Author: CNYALI_LK
LANG: C++
PROG: d.cpp
Mail: cnyalilk@vip.qq.com
*/
#include<bits/stdc++.h>
#define debug(...) fprintf(stderr,__VA_ARGS__)
#define DEBUG printf("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#define Debug debug("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#define all(x) x.begin(),x.end()
#define x first
#define y second
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
const signed inf=0x3f3f3f3f;
const double eps=1e-8;
const double pi=acos(-1.0);
template<class T>int chkmin(T &a,T b){return a>b?a=b,1:0;}
template<class T>int chkmax(T &a,T b){return a<b?a=b,1:0;}
template<class T>T sqr(T a){return a*a;}
template<class T>T mmin(T a,T b){return a<b?a:b;}
template<class T>T mmax(T a,T b){return a>b?a:b;}
template<class T>T aabs(T a){return a<0?-a:a;}
template<class T>int dcmp(T a,T b){return a>b;}
template<int *a>int cmp_a(int x,int y){return a[x]<a[y];}
#define min mmin
#define max mmax
#define abs aabs
namespace io {
	const int SIZE = (1 << 21) + 1;
	char ibuf[SIZE], *iS, *iT, obuf[SIZE], *oS = obuf, *oT = oS + SIZE - 1, c, qu[55]; int f, qr;
	// getchar
	#define gc() (iS == iT ? (iT = (iS = ibuf) + fread (ibuf, 1, SIZE, stdin), (iS == iT ? EOF : *iS ++)) : *iS ++)
	// print the remaining part
	inline void flush () {
		fwrite (obuf, 1, oS - obuf, stdout);
		oS = obuf;
	}
	// putchar
	inline void putc (char x) {
		*oS ++ = x;
		if (oS == oT) flush ();
	}
	// input a signed integer
	inline void read (signed &x) {
		for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;
		for (x = 0; c <= '9' && c >= '0'; c = gc()) x = x * 10 + (c & 15); x *= f;
	}

	inline void read (long long &x) {
		for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;
		for (x = 0; c <= '9' && c >= '0'; c = gc()) x = x * 10 + (c & 15); x *= f;
	}
	inline void read (char &x) {
		x=gc();
	}
	inline void read(char *x){
		while((*x=gc())=='\n' || *x==' '||*x=='\r');
		while(!(*x=='\n'||*x==' '||*x=='\r'))*(++x)=gc();
	}
	template<typename A,typename ...B>
	inline void read(A &x,B &...y){
		read(x);read(y...);
	}
	// print a signed integer
	inline void write (signed x) {
		if (!x) putc ('0'); if (x < 0) putc ('-'), x = -x;
		while (x) qu[++ qr] = x % 10 + '0',  x /= 10;
		while (qr) putc (qu[qr --]);
	}

	inline void write (long long x) {
		if (!x) putc ('0'); if (x < 0) putc ('-'), x = -x;
		while (x) qu[++ qr] = x % 10 + '0',  x /= 10;
		while (qr) putc (qu[qr --]);
	}
	inline void write (char x) {
		putc(x);
	}
	inline void write(const char *x){
		while(*x){putc(*x);++x;}
	}
	inline void write(char *x){
		while(*x){putc(*x);++x;}
	}
	template<typename A,typename ...B>
	inline void write(A x,B ...y){
		write(x);write(y...);
	}
	//no need to call flush at the end manually!
	struct Flusher_ {~Flusher_(){flush();}}io_flusher_;
}
using io :: read;
using io :: putc;
using io :: write;
int fa[200005],siz[200005],t,w[200005],f[19][200005];
int find(int x){return x==fa[x]?x:fa[x]=find(fa[x]);}
int chk(int u,int v,int s){
	for(int i=18;~i;--i)if(w[f[i][u]]<=s)u=f[i][u];
	for(int i=18;~i;--i)if(w[f[i][v]]<=s)v=f[i][v];
	return u==v?siz[u]:siz[u]+siz[v];
}
int main(){
#ifdef cnyali_lk
	freopen("d.in","r",stdin);
	freopen("d.out","w",stdout);
#endif
	int n,m,u,v,q,c;
	read(n,m);
	for(int i=1;i<=n;++i){fa[i]=i;siz[i]=1;}
	t=n;
	for(int i=1;i<=m;++i){
		read(u,v);
		if(find(u)!=find(v)){
			u=find(u);v=find(v);
			siz[fa[u]=fa[v]=++t]=siz[u]+siz[v];
			fa[t]=t;
			w[t]=i;
			f[0][u]=f[0][v]=t;
		}
	}
	w[0]=inf;
	for(int i=1;i<=18;++i)for(int j=1;j<=n+n;++j)f[i][j]=f[i-1][f[i-1][j]];
	read(q);
	for(;q;--q){
		read(u,v,c);	
		int l,r,mid;
		l=0;r=m;mid=0;
		while(l<=r){
			mid=(l+r)>>1;
			if(chk(u,v,mid)>=c)r=mid-1;
			else l=mid+1;
		}
		printf("%d\n",r+1);
	}

	return 0;
}

E

/*
Author: CNYALI_LK
LANG: C++
PROG: e.cpp
Mail: cnyalilk@vip.qq.com
*/
#include<bits/stdc++.h>
#define debug(...) fprintf(stderr,__VA_ARGS__)
#define DEBUG printf("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#define Debug debug("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#define all(x) x.begin(),x.end()
#define x first
#define y second
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
const signed inf=0x3f3f3f3f;
const double eps=1e-8;
const double pi=acos(-1.0);
template<class T>int chkmin(T &a,T b){return a>b?a=b,1:0;}
template<class T>int chkmax(T &a,T b){return a<b?a=b,1:0;}
template<class T>T sqr(T a){return a*a;}
template<class T>T mmin(T a,T b){return a<b?a:b;}
template<class T>T mmax(T a,T b){return a>b?a:b;}
template<class T>T aabs(T a){return a<0?-a:a;}
template<class T>int dcmp(T a,T b){return a>b;}
template<int *a>int cmp_a(int x,int y){return a[x]<a[y];}
#define min mmin
#define max mmax
#define abs aabs
namespace io {
	const int SIZE = (1 << 21) + 1;
	char ibuf[SIZE], *iS, *iT, obuf[SIZE], *oS = obuf, *oT = oS + SIZE - 1, c, qu[55]; int f, qr;
	// getchar
	#define gc() (iS == iT ? (iT = (iS = ibuf) + fread (ibuf, 1, SIZE, stdin), (iS == iT ? EOF : *iS ++)) : *iS ++)
	// print the remaining part
	inline void flush () {
		fwrite (obuf, 1, oS - obuf, stdout);
		oS = obuf;
	}
	// putchar
	inline void putc (char x) {
		*oS ++ = x;
		if (oS == oT) flush ();
	}
	// input a signed integer
	inline void read (signed &x) {
		for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;
		for (x = 0; c <= '9' && c >= '0'; c = gc()) x = x * 10 + (c & 15); x *= f;
	}

	inline void read (long long &x) {
		for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;
		for (x = 0; c <= '9' && c >= '0'; c = gc()) x = x * 10 + (c & 15); x *= f;
	}
	inline void read (char &x) {
		x=gc();
	}
	inline void read(char *x){
		while((*x=gc())=='\n' || *x==' '||*x=='\r');
		while(!(*x=='\n'||*x==' '||*x=='\r'))*(++x)=gc();
	}
	template<typename A,typename ...B>
	inline void read(A &x,B &...y){
		read(x);read(y...);
	}
	// print a signed integer
	inline void write (signed x) {
		if (!x) putc ('0'); if (x < 0) putc ('-'), x = -x;
		while (x) qu[++ qr] = x % 10 + '0',  x /= 10;
		while (qr) putc (qu[qr --]);
	}

	inline void write (long long x) {
		if (!x) putc ('0'); if (x < 0) putc ('-'), x = -x;
		while (x) qu[++ qr] = x % 10 + '0',  x /= 10;
		while (qr) putc (qu[qr --]);
	}
	inline void write (char x) {
		putc(x);
	}
	inline void write(const char *x){
		while(*x){putc(*x);++x;}
	}
	inline void write(char *x){
		while(*x){putc(*x);++x;}
	}
	template<typename A,typename ...B>
	inline void write(A x,B ...y){
		write(x);write(y...);
	}
	//no need to call flush at the end manually!
	struct Flusher_ {~Flusher_(){flush();}}io_flusher_;
}
using io :: read;
using io :: putc;
using io :: write;
int a[100005],n;
void judge(int x){
	int cnt=0;
	for(int y=x+1;a[y]==x && y<n;++y){
		cnt^=1;	
	}
	if(cnt || (a[x]-x)&1)printf("First\n");
	else printf("Second\n");
}
int main(){
#ifdef cnyali_lk
	freopen("e.in","r",stdin);
	freopen("e.out","w",stdout);
#endif
	read(n);
	for(int i=0;i<n;++i){read(a[i]);--a[i];}
	sort(a,a+n,dcmp<int>);
	for(int i=0;i<n;++i)if(a[i+1]<i+1){judge(i);return 0; }
	return 0;
}

F

/*
Author: CNYALI_LK
LANG: C++
PROG: f.cpp
Mail: cnyalilk@vip.qq.com
*/
#include<bits/stdc++.h>
#define debug(...) fprintf(stderr,__VA_ARGS__)
#define DEBUG printf("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#define Debug debug("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#define all(x) x.begin(),x.end()
#define x first
#define y second
#define int long long
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
const signed inf=0x3f3f3f3f;
const double eps=1e-8;
const double pi=acos(-1.0);
template<class T>int chkmin(T &a,T b){return a>b?a=b,1:0;}
template<class T>int chkmax(T &a,T b){return a<b?a=b,1:0;}
template<class T>T sqr(T a){return a*a;}
template<class T>T mmin(T a,T b){return a<b?a:b;}
template<class T>T mmax(T a,T b){return a>b?a:b;}
template<class T>T aabs(T a){return a<0?-a:a;}
template<class T>int dcmp(T a,T b){return a>b;}
template<int *a>int cmp_a(int x,int y){return a[x]<a[y];}
#define min mmin
#define max mmax
#define abs aabs
namespace io {
	const int SIZE = (1 << 21) + 1;
	char ibuf[SIZE], *iS, *iT, obuf[SIZE], *oS = obuf, *oT = oS + SIZE - 1, c, qu[55]; int f, qr;
	// getchar
	#define gc() (iS == iT ? (iT = (iS = ibuf) + fread (ibuf, 1, SIZE, stdin), (iS == iT ? EOF : *iS ++)) : *iS ++)
	// print the remaining part
	inline void flush () {
		fwrite (obuf, 1, oS - obuf, stdout);
		oS = obuf;
	}
	// putchar
	inline void putc (char x) {
		*oS ++ = x;
		if (oS == oT) flush ();
	}
	// input a signed integer
	inline void read (signed &x) {
		for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;
		for (x = 0; c <= '9' && c >= '0'; c = gc()) x = x * 10 + (c & 15); x *= f;
	}

	inline void read (long long &x) {
		for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;
		for (x = 0; c <= '9' && c >= '0'; c = gc()) x = x * 10 + (c & 15); x *= f;
	}
	inline void read (char &x) {
		x=gc();
	}
	inline void read(char *x){
		while((*x=gc())=='\n' || *x==' '||*x=='\r');
		while(!(*x=='\n'||*x==' '||*x=='\r'))*(++x)=gc();
	}
	template<typename A,typename ...B>
	inline void read(A &x,B &...y){
		read(x);read(y...);
	}
	// print a signed integer
	inline void write (signed x) {
		if (!x) putc ('0'); if (x < 0) putc ('-'), x = -x;
		while (x) qu[++ qr] = x % 10 + '0',  x /= 10;
		while (qr) putc (qu[qr --]);
	}

	inline void write (long long x) {
		if (!x) putc ('0'); if (x < 0) putc ('-'), x = -x;
		while (x) qu[++ qr] = x % 10 + '0',  x /= 10;
		while (qr) putc (qu[qr --]);
	}
	inline void write (char x) {
		putc(x);
	}
	inline void write(const char *x){
		while(*x){putc(*x);++x;}
	}
	inline void write(char *x){
		while(*x){putc(*x);++x;}
	}
	template<typename A,typename ...B>
	inline void write(A x,B ...y){
		write(x);write(y...);
	}
	//no need to call flush at the end manually!
	struct Flusher_ {~Flusher_(){flush();}}io_flusher_;
}
using io :: read;
using io :: putc;
using io :: write;
int fac[4000005],inv[4000005],invf[4000005];
int f[2005][2005];
const int p=1000000007;
int C(int a,int b){return a<0||a<b||b<0?0:fac[a]*invf[b]%p*invf[a-b]%p;}
signed main(){
#ifdef cnyali_lk
	freopen("f.in","r",stdin);
	freopen("f.out","w",stdout);
#endif
	int n,k;	
	read(n,k);
	if(k==1)return printf("1\n"),0;
	fac[0]=fac[1]=inv[1]=invf[0]=invf[1]=1;
	for(int i=2;i<=n*k;++i){
		fac[i]=fac[i-1]*i%p;
		inv[i]=(p-p/i)*inv[p%i]%p;
		invf[i]=inv[i]*invf[i-1]%p;
	}
	f[0][0]=1;
	for(int i=1;i<=n;++i){
		f[i][0]=1;
		for(int j=1;j<=i;++j){
			f[i][j]=(f[i-1][j]+f[i][j-1]*C(n-i+(n-j+1)*(k-1)-1,k-2))%p;
//			write(f[i][j],j==i?'\n':' ');
//			write('(',n-i+(n-j+1)*(k-1),',',j-1,")=",C(n-i+(n-j+1)*(k-1),j-1),j==i?'\n':' ');
		}
	}
	write(f[n][n]*(k>1?fac[n]:1)%p,'\n');
	return 0;
}