排列組合問題 參考官方題解
/\*
\* GCA : "Computer is artificial subject absolutely,Math is God"
\*/
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <climits>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <cctype>
#include <utility>
#include <ctime>
using namespace std;
#ifdef DEBUG
#define VAR(a,b) \_\_typeof(b) a=(b)
#define debug(...) printf("DEBUG: "),printf(\_\_VA\_ARGS\_\_)
#else
#define VAR(a,b) \_\_typeof(b) a=(b)
#define debug(...)
#endif
typedef unsigned int uint;
typedef long long int Int;
typedef unsigned long long int UInt;
#define Set(a,s) memset(a,s,sizeof(a))
#define Pln() printf("\\n")
#define For(i,x)for(int i=0;i<x;i++)
#define CON(x,y) x##y
#define M 1105
#define PB push\_back
#define oo INT\_MAX
#define FOR(a,b) for(VAR(a,(b).begin());a!=(b).end();++a)
#define eps 1e-9
#define X first
#define Y second
inline bool xdy(double x,double y){return x>y+eps;}
inline bool xddy(double x,double y){return x>y-eps;}
inline bool xcy(double x,double y){return x<y-eps;}
inline bool xcdy(double x,double y){return x<y+eps;}
const Int mod=1000000007;
int n,m;
Int c\[M\]\[M\];
void init(){
c\[0\]\[0\]=1;
for(int i=1;i<M;i++){
c\[i\]\[0\]=1;
for(int j=1;j<=i;j++){
c\[i\]\[j\]=(c\[i-1\]\[j\]+c\[i-1\]\[j-1\])%mod;
}
}
}
Int d\[M\];
Int powmod(Int b,Int n){
if(n<0)return 1;
Int ans=1,base\=b;
while(n){
if(n&1)ans=(ans\*base)%mod;
base\=(base\*base)%mod;
n>>=1;
}
return ans;
}
int main() {
ios\_base::sync\_with\_stdio(0);
init();
while(~scanf("%d%d",&n,&m)){
Int all;
Set(d,0);
d\[0\]=0;
for(int i=1;i<=m;i++){
scanf("%I64d",&d\[i\]);
}
sort(d,d+m+1);
all=n-m;
Int ans=1;
// for(int i=1;i<=m;i++)debug("I"
for(int i=1;i<=m;i++){
ans=(ans\*c\[all\]\[d\[i\]-d\[i-1\]-1\])%mod;
// debug("%I64d %I64d %I64d\\n",all,d\[i\]-d\[i-1\]-1,c\[all\]\[d\[i\]-d\[i-1\]-1\]);
if(i!=1){
// debug("ok");
ans=(ans\*powmod(2,d\[i\]-d\[i-1\]-2))%mod;
}
all-=d\[i\]-d\[i-1\]-1;
}
printf("%I64d\\n",ans);
}
}