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

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/*
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

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/*
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

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/*
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

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/*
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

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/*
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

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/*
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;
}

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