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ID题目提交者结果用时内存语言文件大小提交时间测评时间
#810649#6137. Sub-cycle GraphhotdogsellerAC ✓241ms7104kbC++141.9kb2024-12-12 07:52:132024-12-12 07:52:14

Judging History

你现在查看的是最新测评结果

  • [2024-12-12 07:52:14]
  • 评测
  • 测评结果:AC
  • 用时:241ms
  • 内存:7104kb
  • [2024-12-12 07:52:13]
  • 提交

answer

#include<bits/stdc++.h>

#define maxn 100005
#define int long long
#define mod 1000000007

using namespace std;

inline int read(){
	int lre=0,f=1;
	char c=getchar();
	while(!isdigit(c)){
		if(c=='-'){
			f=-1;
		}
		c=getchar();
	}
	while(isdigit(c)){
		lre=(lre<<3)+(lre<<1)+(c-'0');
		c=getchar();
	}
	return lre*f;
}

inline int slowpow(int a,int b){
	__int128 x=a,y=b;
	return (x*y)%mod;
}

inline int quickpow(int a,int b){
	int lre=1;
	while(b){
		if(b&1)lre=slowpow(lre,a);
		b>>=1;
		a=slowpow(a,a); 
	}
	return lre;
}

int n,m,res;
int fact[maxn],inv[maxn];
//n个点全部在链上,i条链,方案数:C(n,2i)*i^(n-2i)/2^i

int pw[maxn],pv[maxn];//2^i和2^-i 

int C(int a,int b){
	if(b==0)return 1;
	if(b>a)return 0;
	int lre=slowpow(slowpow(fact[a],inv[b]),inv[a-b]);
//	cout<<"C("<<a<<","<<b<<")="<<lre<<endl;
	return lre;
} 

void solve(){
	n=read();m=read();
	if(m>n){cout<<0<<endl;return;}
	if(m==n){
		//(n-1)!/2
		printf("%lld\n",slowpow(fact[n-1],inv[2]));
		return;
	}
	int k=n-m;
	res=pv[k];int lre=0;
//	cout<<"k="<<k<<endl;
	for(int i=0;i<=n-k;i++){
		//((k&1)?-1:1)*C(a,k)*pw[a-k]*C(n-k-1,n-a-k)
		int tmp=slowpow(C(k,i),slowpow(pw[k-i],C(n-i-1,k-1)));
		if(i&1){
			lre=(lre-tmp+mod)%mod;
		}else{
			lre=(lre+tmp)%mod;
		}
	}
	res=slowpow(res,lre);
	res=slowpow(slowpow(res,fact[n]),inv[k]);
	printf("%lld\n",res);
}

signed main(){
	
	fact[0]=inv[0]=1;
	pw[0]=pv[0]=1;
	for(int i=1;i<=100000;i++){
		fact[i]=slowpow(fact[i-1],i);
		pw[i]=slowpow(pw[i-1],2);
	}
	inv[100000]=quickpow(fact[100000],mod-2);
	pv[100000]=quickpow(pw[100000],mod-2);
	for(int i=100000;i>=1;--i){
		inv[i-1]=slowpow(inv[i],i);
		pv[i-1]=slowpow(pv[i],2);
	}
	
	for(int i=1;i<=10;i++){
	//	cout<<pw[i]<<" "<<fact[i]<<endl;
		assert(slowpow(pw[i],pv[i])==1);
		assert(slowpow(fact[i],inv[i])==1); 
	}
	
	int t=read();
	while(t--){
		solve(); 
	}
	
	return 0;
}

詳細信息

Test #1:

score: 100
Accepted
time: 0ms
memory: 6912kb

input:

3
4 2
4 3
5 3

output:

15
12
90

result:

ok 3 number(s): "15 12 90"

Test #2:

score: 0
Accepted
time: 241ms
memory: 7104kb

input:

17446
3 0
3 1
3 2
3 3
4 0
4 1
4 2
4 3
4 4
5 0
5 1
5 2
5 3
5 4
5 5
6 0
6 1
6 2
6 3
6 4
6 5
6 6
7 0
7 1
7 2
7 3
7 4
7 5
7 6
7 7
8 0
8 1
8 2
8 3
8 4
8 5
8 6
8 7
8 8
9 0
9 1
9 2
9 3
9 4
9 5
9 6
9 7
9 8
9 9
10 0
10 1
10 2
10 3
10 4
10 5
10 6
10 7
10 8
10 9
10 10
11 0
11 1
11 2
11 3
11 4
11 5
11 6
11 7
11...

output:

1
3
3
1
1
6
15
12
3
1
10
45
90
60
12
1
15
105
375
630
360
60
1
21
210
1155
3465
5040
2520
360
1
28
378
2940
13545
35280
45360
20160
2520
1
36
630
6552
42525
170100
393120
453600
181440
20160
1
45
990
13230
114345
643545
2286900
4762800
4989600
1814400
181440
1
55
1485
24750
273735
2047815
10239075
3...

result:

ok 17446 numbers