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#556343#9254. Random Variablesforgive_TL 4ms11712kbC++141.2kb2024-09-10 17:08:272024-09-10 17:08:27

Judging History

This is the latest submission verdict.

  • [2024-09-10 17:08:27]
  • Judged
  • Verdict: TL
  • Time: 4ms
  • Memory: 11712kb
  • [2024-09-10 17:08:27]
  • Submitted

answer

#include <bits/stdc++.h>
using namespace std ;

typedef long long LL ;
const int N = 1010 ;
// 妙妙题
// 容斥可以完成这个计数
// 观察dp式子,m每减1,n会减k,所以复杂度是 n/k 的 

int T , mod ;
LL C[N][N] ;

unordered_map<int,LL> f[N] ;
int K , n , m ;
LL dp( int n , int m ) // n个不同小球放入 m 个箱子,要求每个箱子中球数 <= K 
{
	if( n < 0 ) return 0 ;
	if( m == 1 ) return (n<=K) ;
	if( n == 0 ) return 1 ;
	if( f[n].count(m) ) return f[n][m] ;
//	printf("f[%d][%d] = %lld\n" , n , m , f[n][m] ) ;
	return f[n][m] = m*( dp(n-1,m) - dp(n-K-1,m-1)*C[n-1][K]%mod ) % mod ;
//	return f[n][m] ;
}

int main()
{
	scanf("%d%d" , &T , &mod ) ;
	for(int i = 0 ; i <= 1000 ; 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 ;
		}
	}
	while( T -- ) {
		scanf("%d%d" , &n , &m ) ;
		LL sum = 0 , pw = 1 ;
		for( K = 1 ; K < n ; K ++ ) {
			for(int i = 0 ; i <= n ; i ++ ) f[i].clear() ;
			sum = ( sum + dp(n,m) ) % mod ;
//			printf("K = %d , (%d,%d) = %lld\n" , K , n , m , dp(n,m) ) ;
			pw = pw * m % mod ;
		}
		pw = pw * m % mod ;
		printf("%lld\n" , (pw*n%mod - sum + mod ) % mod ) ;
	}
	return 0 ;
}

詳細信息

Test #1:

score: 100
Accepted
time: 3ms
memory: 11372kb

input:

3 123456789
3 2
5 5
7 7

output:

18
7145
2066323

result:

ok 3 lines

Test #2:

score: 0
Accepted
time: 0ms
memory: 11056kb

input:

100 2
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
1 10
2 1
2 2
2 3
2 4
2 5
2 6
2 7
2 8
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2 10
3 1
3 2
3 3
3 4
3 5
3 6
3 7
3 8
3 9
3 10
4 1
4 2
4 3
4 4
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4 7
4 8
4 9
4 10
5 1
5 2
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5 7
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5 10
6 1
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6 8
6 9
6 10
7 1
7 2
7 3
7 4
7 5
7 6
7 7
7 8
7 9
7 10
8 1
8 2...

output:

1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
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1
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1
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1
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0
1
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1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0

result:

ok 100 lines

Test #3:

score: 0
Accepted
time: 4ms
memory: 11712kb

input:

100 3
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
1 10
2 1
2 2
2 3
2 4
2 5
2 6
2 7
2 8
2 9
2 10
3 1
3 2
3 3
3 4
3 5
3 6
3 7
3 8
3 9
3 10
4 1
4 2
4 3
4 4
4 5
4 6
4 7
4 8
4 9
4 10
5 1
5 2
5 3
5 4
5 5
5 6
5 7
5 8
5 9
5 10
6 1
6 2
6 3
6 4
6 5
6 6
6 7
6 8
6 9
6 10
7 1
7 2
7 3
7 4
7 5
7 6
7 7
7 8
7 9
7 10
8 1
8 2...

output:

1
2
0
1
2
0
1
2
0
1
2
0
0
2
0
0
2
0
0
2
0
0
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1
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1
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1
2
2
0
2
2
0
2
2
0
2
0
0
0
0
0
0
0
0
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1
0
0
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0
1
0
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1
2
2
0
2
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
2
0
1

result:

ok 100 lines

Test #4:

score: 0
Accepted
time: 0ms
memory: 11376kb

input:

100 4
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
1 10
2 1
2 2
2 3
2 4
2 5
2 6
2 7
2 8
2 9
2 10
3 1
3 2
3 3
3 4
3 5
3 6
3 7
3 8
3 9
3 10
4 1
4 2
4 3
4 4
4 5
4 6
4 7
4 8
4 9
4 10
5 1
5 2
5 3
5 4
5 5
5 6
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5 8
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5 10
6 1
6 2
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6 8
6 9
6 10
7 1
7 2
7 3
7 4
7 5
7 6
7 7
7 8
7 9
7 10
8 1
8 2...

output:

1
2
3
0
1
2
3
0
1
2
2
2
0
0
2
2
0
0
2
2
3
2
3
0
3
2
3
0
3
2
0
0
0
0
0
0
0
0
0
0
1
2
3
0
1
2
3
0
1
2
2
0
2
0
2
0
2
0
2
0
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0
3
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3
0
3
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3
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0
0
0
0
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0
0
0
0
1
2
3
0
1
2
3
0
1
2
2
0
2
0
2
0
2
0
2
0

result:

ok 100 lines

Test #5:

score: 0
Accepted
time: 0ms
memory: 11460kb

input:

100 5
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
1 10
2 1
2 2
2 3
2 4
2 5
2 6
2 7
2 8
2 9
2 10
3 1
3 2
3 3
3 4
3 5
3 6
3 7
3 8
3 9
3 10
4 1
4 2
4 3
4 4
4 5
4 6
4 7
4 8
4 9
4 10
5 1
5 2
5 3
5 4
5 5
5 6
5 7
5 8
5 9
5 10
6 1
6 2
6 3
6 4
6 5
6 6
6 7
6 8
6 9
6 10
7 1
7 2
7 3
7 4
7 5
7 6
7 7
7 8
7 9
7 10
8 1
8 2...

output:

1
2
3
4
0
1
2
3
4
0
2
1
2
0
0
2
1
2
0
0
3
3
1
3
0
3
3
1
3
0
4
4
2
4
0
4
4
2
4
0
0
0
0
0
0
0
0
0
0
0
1
2
3
4
0
1
2
3
4
0
2
3
3
2
0
2
3
3
2
0
3
4
1
2
0
3
4
1
2
0
4
4
4
4
0
4
4
4
4
0
0
0
0
0
0
0
0
0
0
0

result:

ok 100 lines

Test #6:

score: 0
Accepted
time: 0ms
memory: 11396kb

input:

100 6
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
1 10
2 1
2 2
2 3
2 4
2 5
2 6
2 7
2 8
2 9
2 10
3 1
3 2
3 3
3 4
3 5
3 6
3 7
3 8
3 9
3 10
4 1
4 2
4 3
4 4
4 5
4 6
4 7
4 8
4 9
4 10
5 1
5 2
5 3
5 4
5 5
5 6
5 7
5 8
5 9
5 10
6 1
6 2
6 3
6 4
6 5
6 6
6 7
6 8
6 9
6 10
7 1
7 2
7 3
7 4
7 5
7 6
7 7
7 8
7 9
7 10
8 1
8 2...

output:

1
2
3
4
5
0
1
2
3
4
2
0
0
2
0
0
2
0
0
2
3
0
3
0
3
0
3
0
3
0
4
2
0
4
2
0
4
2
0
4
5
2
3
2
5
0
5
2
3
2
0
0
0
0
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0
0
0
0
0
1
0
3
4
3
0
1
0
3
4
2
2
0
2
2
0
2
2
0
2
3
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3
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3
0
3
0
3
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4
2
0
4
2
0
4
2
0
4

result:

ok 100 lines

Test #7:

score: 0
Accepted
time: 4ms
memory: 11648kb

input:

100 7
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
1 10
2 1
2 2
2 3
2 4
2 5
2 6
2 7
2 8
2 9
2 10
3 1
3 2
3 3
3 4
3 5
3 6
3 7
3 8
3 9
3 10
4 1
4 2
4 3
4 4
4 5
4 6
4 7
4 8
4 9
4 10
5 1
5 2
5 3
5 4
5 5
5 6
5 7
5 8
5 9
5 10
6 1
6 2
6 3
6 4
6 5
6 6
6 7
6 8
6 9
6 10
7 1
7 2
7 3
7 4
7 5
7 6
7 7
7 8
7 9
7 10
8 1
8 2...

output:

1
2
3
4
5
6
0
1
2
3
2
6
5
6
2
0
0
2
6
5
3
4
2
3
6
3
0
3
4
2
4
2
3
5
2
5
0
4
2
3
5
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3
6
5
4
0
5
5
3
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0
6
1
1
6
0
6
0
6
0
0
0
0
0
0
0
0
0
0
1
2
3
4
5
6
0
1
2
3
2
1
4
4
1
2
0
2
1
4
3
3
4
3
4
4
0
3
3
4

result:

ok 100 lines

Test #8:

score: 0
Accepted
time: 4ms
memory: 11428kb

input:

100 8
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
1 10
2 1
2 2
2 3
2 4
2 5
2 6
2 7
2 8
2 9
2 10
3 1
3 2
3 3
3 4
3 5
3 6
3 7
3 8
3 9
3 10
4 1
4 2
4 3
4 4
4 5
4 6
4 7
4 8
4 9
4 10
5 1
5 2
5 3
5 4
5 5
5 6
5 7
5 8
5 9
5 10
6 1
6 2
6 3
6 4
6 5
6 6
6 7
6 8
6 9
6 10
7 1
7 2
7 3
7 4
7 5
7 6
7 7
7 8
7 9
7 10
8 1
8 2...

output:

1
2
3
4
5
6
7
0
1
2
2
6
4
4
6
2
0
0
2
6
3
2
3
4
3
6
3
0
3
2
4
4
0
0
4
4
0
0
4
4
5
6
3
4
1
2
7
0
5
6
6
4
6
0
6
4
6
0
6
4
7
4
3
0
7
4
3
0
7
4
0
0
0
0
0
0
0
0
0
0
1
6
3
4
5
2
7
0
1
6
2
4
6
0
2
4
6
0
2
4

result:

ok 100 lines

Test #9:

score: 0
Accepted
time: 4ms
memory: 11372kb

input:

100 9
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
1 10
2 1
2 2
2 3
2 4
2 5
2 6
2 7
2 8
2 9
2 10
3 1
3 2
3 3
3 4
3 5
3 6
3 7
3 8
3 9
3 10
4 1
4 2
4 3
4 4
4 5
4 6
4 7
4 8
4 9
4 10
5 1
5 2
5 3
5 4
5 5
5 6
5 7
5 8
5 9
5 10
6 1
6 2
6 3
6 4
6 5
6 6
6 7
6 8
6 9
6 10
7 1
7 2
7 3
7 4
7 5
7 6
7 7
7 8
7 9
7 10
8 1
8 2...

output:

1
2
3
4
5
6
7
8
0
1
2
6
3
2
3
6
2
0
0
2
3
0
6
0
6
3
6
3
0
3
4
8
3
4
5
6
4
2
0
4
5
2
0
2
8
0
8
5
0
5
6
0
0
6
0
0
6
0
0
6
7
3
6
1
3
3
4
3
0
7
8
8
6
5
8
3
2
8
0
8
0
0
0
0
0
0
0
0
0
0
1
8
3
4
2
6
7
5
0
1

result:

ok 100 lines

Test #10:

score: 0
Accepted
time: 0ms
memory: 11420kb

input:

100 10
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
1 10
2 1
2 2
2 3
2 4
2 5
2 6
2 7
2 8
2 9
2 10
3 1
3 2
3 3
3 4
3 5
3 6
3 7
3 8
3 9
3 10
4 1
4 2
4 3
4 4
4 5
4 6
4 7
4 8
4 9
4 10
5 1
5 2
5 3
5 4
5 5
5 6
5 7
5 8
5 9
5 10
6 1
6 2
6 3
6 4
6 5
6 6
6 7
6 8
6 9
6 10
7 1
7 2
7 3
7 4
7 5
7 6
7 7
7 8
7 9
7 10
8 1
8 ...

output:

1
2
3
4
5
6
7
8
9
0
2
6
2
0
0
2
6
2
0
0
3
8
1
8
5
8
3
6
3
0
4
4
2
4
0
4
4
2
4
0
5
0
5
0
5
0
5
0
5
0
6
2
8
4
0
6
2
8
4
0
7
8
3
2
5
2
3
8
7
0
8
4
6
2
0
8
4
6
2
0
9
4
9
4
5
4
9
4
9
0
0
0
0
0
0
0
0
0
0
0

result:

ok 100 lines

Test #11:

score: 0
Accepted
time: 4ms
memory: 11472kb

input:

100 11
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
1 10
2 1
2 2
2 3
2 4
2 5
2 6
2 7
2 8
2 9
2 10
3 1
3 2
3 3
3 4
3 5
3 6
3 7
3 8
3 9
3 10
4 1
4 2
4 3
4 4
4 5
4 6
4 7
4 8
4 9
4 10
5 1
5 2
5 3
5 4
5 5
5 6
5 7
5 8
5 9
5 10
6 1
6 2
6 3
6 4
6 5
6 6
6 7
6 8
6 9
6 10
7 1
7 2
7 3
7 4
7 5
7 6
7 7
7 8
7 9
7 10
8 1
8 ...

output:

1
2
3
4
5
6
7
8
9
10
2
6
1
9
8
9
1
6
2
0
3
7
7
9
8
10
10
3
6
3
4
0
5
5
10
10
8
9
9
6
5
0
4
10
6
7
10
4
2
7
6
10
4
5
3
2
0
7
2
5
7
5
2
8
6
1
6
0
3
6
8
6
6
3
2
4
8
3
6
9
9
8
10
2
8
6
10
9
3
1
10
0
4
3
0
6
0
7
4
9

result:

ok 100 lines

Test #12:

score: -100
Time Limit Exceeded

input:

10 972033073
576 523187654
758 588616188
30 532959085
476 481773028
573 76725430
520 142462406
865 820120297
687 526533288
913 38106557
67 924529654

output:


result: