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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#841032#9254. Random VariablesHthntdTL 900ms16760kbC++201.3kb2025-01-03 11:25:562025-01-03 11:25:58

Judging History

This is the latest submission verdict.

  • [2025-01-03 11:25:58]
  • Judged
  • Verdict: TL
  • Time: 900ms
  • Memory: 16760kb
  • [2025-01-03 11:25:56]
  • Submitted

answer

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

const int N = 1e3 + 10;
int T, mod, C[N][N];
unordered_map<int,int> q[N];

ll quick_pow(ll x, int y){
	ll res = 1;
	while(y){
		if(y & 1) res = res * x % mod;
		x = x * x % mod;
		y >>= 1;
	}
	return res;
}

void pre(){
	C[0][0] = 1;
	for(int i = 1; i < N; ++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;
	}
	return;
}

int dfs(int x, int y, int lim){
	if(x < 0 || !lim) return 0;
	if(x == 0) return 1;
	if(x == 1) return y;
	if(q[x].find(y) != q[x].end()) return q[x][y];
	return q[x][y] = (1ll * y * dfs(x - 1, y, lim) % mod - 1ll * dfs(x - lim - 1, y - 1, lim) * C[x - 1][lim] % mod * y % mod + mod) % mod;
}

signed main()
{
	// freopen(".in","r",stdin);
	// freopen(".out","w",stdout);
	// int st = clock();
	cin >> T >> mod;
	pre();
	while(T--){
		int n, m;
		scanf("%d%d", &n, &m);
		ll res = 0, S = quick_pow(m, n);
		for(int i = 0; i <= n; ++i){
			for(int j = 0; j <= n; ++j){
				auto it = q[j].begin();
				while(it != q[j].end()) it = q[j].erase(it);
			}
			res = (res + S - dfs(n, m, i) % mod) % mod;
		}
		printf("%lld\n", (res + mod) % mod);
	}
	// int en = clock();
	// cerr << en - st << '\n';
	return 0;
}
/*
3 123456789
3 2
5 5
7 7
*/

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 2ms
memory: 7852kb

input:

3 123456789
3 2
5 5
7 7

output:

18
7145
2066323

result:

ok 3 lines

Test #2:

score: 0
Accepted
time: 3ms
memory: 7848kb

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
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
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
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1
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0
0
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0
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1
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1
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1
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1
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1
0
0
0
0
0
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0
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0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
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0
0
0
0
0
0
0
1
0
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: 2ms
memory: 7852kb

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
0
0
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0
0
0
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1
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0
1
2
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1
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0
2
2
0
2
2
0
2
0
0
0
0
0
0
0
0
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1
0
0
1
0
0
1
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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: 8144kb

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
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
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
3
0
3
0
3
0
3
0
3
0
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

result:

ok 100 lines

Test #5:

score: 0
Accepted
time: 2ms
memory: 8148kb

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: 2ms
memory: 7852kb

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

result:

ok 100 lines

Test #7:

score: 0
Accepted
time: 0ms
memory: 7920kb

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
5
3
6
5
4
0
5
5
3
6
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: 2ms
memory: 8152kb

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: 2ms
memory: 8140kb

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: 8140kb

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: 2ms
memory: 7796kb

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: 0
Accepted
time: 900ms
memory: 16760kb

input:

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

output:

259748390
909910217
708973357
300073565
463921261
889897372
587262932
255642402
868975954
14589849

result:

ok 10 lines

Test #13:

score: -100
Time Limit Exceeded

input:

10 922366485
846 278501607
683 609355362
44 978777279
545 730718412
926 323835432
883 761846029
623 408215612
989 588832935
449 743830620
259 183431187

output:


result: