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Submission #744307

# Submission time Handle Problem Language Result Execution time Memory
744307 2023-05-18T11:17:24 Z MohamedAhmed04 Magneti (COCI21_magneti) C++14
110 / 110
 171 ms 55892 KB 
#include <bits/stdc++.h>

using namespace std ;

const int mod = 1e9 + 7 ;

int Add(int x , int y)
{
	int z = x + y ;
	if(z >= mod)
		z -= mod ;
	return z ;
}

int Sub(int x , int y)
{
	int z = x - y ;
	if(z < 0)
		z += mod ;
	return z ;
}

int Mul(int x , int y)
{
	return (x * 1ll * y) % mod ;
}

int powlog(int base , int power)
{
	if(power == 0)
		return 1 ;
	int x = powlog(base , power / 2) ;
	x = Mul(x , x) ;
	if(power & 1)
		x = Mul(x , base) ;
	return x ;
}

int modinv(int x)
{
	return powlog(x , mod-2) ;
}

int Div(int x , int y)
{
	return Mul(x , modinv(y)) ;
}

struct combination
{
    vector<int>fact , inv ;
    combination(int sz) : fact(sz + 1) , inv(sz + 1)
    {
        fact[0] = 1 ;
        inv[0] = 1 ;
        for(int i = 1 ; i <= sz ; ++i)
            fact[i] = Mul(fact[i-1] , i) ;
        inv[sz] = modinv(fact[sz]) ;
		for(int i = sz-1 ; i >= 1 ; --i)
		    inv[i] = Mul(inv[i+1] , i+1) ;
    }
    int choose(int n , int k) const
    {
        if(k < 0 || n < k)
            return 0 ;
        return Mul(Mul(fact[n] , inv[k]) , inv[n - k]) ;
    }
};

const int MAX = 2e4 + 10 ;
const int MAXN = 50 + 10 ;

combination comb(MAX) ;

int arr[MAXN] ;
int n , m ;

int dp[MAXN][MAXN][MAX] ;

int stars_and_bars(int n , int k)
{
	return comb.choose(n+k-1 , k-1) ;
}

int main()
{
	ios_base::sync_with_stdio(0) ;
	cin.tie(0) ;
	cin>>n>>m ;
	for(int i = 1 ; i <= n ; ++i)
		cin>>arr[i] ;
	sort(arr+1 , arr+n+1) ;
	dp[0][0][0] = 1 ;
	for(int i = 1 ; i <= n ; ++i)
	{
		for(int j = 1 ; j <= i ; ++j)
		{
			for(int k = 0 ; k <= m ; ++k)
			{
				dp[i][j][k] = Mul(dp[i-1][j-1][k] , j) ;
				if(k >= arr[i]-1)
					dp[i][j][k] = Add(dp[i][j][k] , Mul(2 , Mul(dp[i-1][j][k-(arr[i]-1)] , j))) ;
				if(k >= 2*(arr[i]-1))
					dp[i][j][k] = Add(dp[i][j][k] , Mul(dp[i-1][j+1][k-2*(arr[i]-1)] , j)) ;
			}
		}
	}
	int ans = 0 ;
	for(int k = 0 ; k+n <= m ; ++k)
		ans = Add(ans , Mul(dp[n][1][k] , stars_and_bars(m-k-n , n+1))) ;
	return cout<<ans<<"\n" , 0 ;
}

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 154 ms 55788 KB Output is correct
2 Correct 4 ms 6100 KB Output is correct
3 Correct 8 ms 2900 KB Output is correct
4 Correct 3 ms 852 KB Output is correct
5 Correct 10 ms 4192 KB Output is correct
6 Correct 45 ms 16684 KB Output is correct
7 Correct 40 ms 30204 KB Output is correct
8 Correct 1 ms 468 KB Output is correct
9 Correct 14 ms 15068 KB Output is correct
10 Correct 1 ms 468 KB Output is correct

Subtask #2
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 2900 KB Output is correct
2 Correct 2 ms 596 KB Output is correct
3 Correct 8 ms 2876 KB Output is correct
4 Correct 2 ms 724 KB Output is correct
5 Correct 7 ms 2792 KB Output is correct
6 Correct 2 ms 852 KB Output is correct
7 Correct 8 ms 2900 KB Output is correct
8 Correct 1 ms 852 KB Output is correct
9 Correct 1 ms 852 KB Output is correct
10 Correct 1 ms 468 KB Output is correct

Subtask #3
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 3056 KB Output is correct
2 Correct 2 ms 1492 KB Output is correct
3 Correct 3 ms 3052 KB Output is correct
4 Correct 2 ms 1748 KB Output is correct
5 Correct 3 ms 3028 KB Output is correct
6 Correct 1 ms 1364 KB Output is correct
7 Correct 4 ms 3048 KB Output is correct
8 Correct 1 ms 724 KB Output is correct
9 Correct 2 ms 1640 KB Output is correct
10 Correct 1 ms 724 KB Output is correct

Subtask #4
50.0 / 50.0

# Verdict Execution time Memory Grader output
1 Correct 154 ms 55788 KB Output is correct
2 Correct 4 ms 6100 KB Output is correct
3 Correct 8 ms 2900 KB Output is correct
4 Correct 3 ms 852 KB Output is correct
5 Correct 10 ms 4192 KB Output is correct
6 Correct 45 ms 16684 KB Output is correct
7 Correct 40 ms 30204 KB Output is correct
8 Correct 1 ms 468 KB Output is correct
9 Correct 14 ms 15068 KB Output is correct
10 Correct 1 ms 468 KB Output is correct
11 Correct 8 ms 2900 KB Output is correct
12 Correct 2 ms 596 KB Output is correct
13 Correct 8 ms 2876 KB Output is correct
14 Correct 2 ms 724 KB Output is correct
15 Correct 7 ms 2792 KB Output is correct
16 Correct 2 ms 852 KB Output is correct
17 Correct 8 ms 2900 KB Output is correct
18 Correct 1 ms 852 KB Output is correct
19 Correct 1 ms 852 KB Output is correct
20 Correct 1 ms 468 KB Output is correct
21 Correct 3 ms 3056 KB Output is correct
22 Correct 2 ms 1492 KB Output is correct
23 Correct 3 ms 3052 KB Output is correct
24 Correct 2 ms 1748 KB Output is correct
25 Correct 3 ms 3028 KB Output is correct
26 Correct 1 ms 1364 KB Output is correct
27 Correct 4 ms 3048 KB Output is correct
28 Correct 1 ms 724 KB Output is correct
29 Correct 2 ms 1640 KB Output is correct
30 Correct 1 ms 724 KB Output is correct
31 Correct 151 ms 55764 KB Output is correct
32 Correct 92 ms 35404 KB Output is correct
33 Correct 171 ms 55796 KB Output is correct
34 Correct 31 ms 12172 KB Output is correct
35 Correct 154 ms 55720 KB Output is correct
36 Correct 9 ms 3784 KB Output is correct
37 Correct 151 ms 55708 KB Output is correct
38 Correct 30 ms 13328 KB Output is correct
39 Correct 150 ms 55732 KB Output is correct
40 Correct 55 ms 16896 KB Output is correct
41 Correct 152 ms 55892 KB Output is correct
42 Correct 1 ms 872 KB Output is correct
43 Correct 143 ms 55768 KB Output is correct
44 Correct 15 ms 6244 KB Output is correct
45 Correct 145 ms 55804 KB Output is correct
46 Correct 1 ms 548 KB Output is correct
47 Correct 26 ms 17272 KB Output is correct
48 Correct 12 ms 10212 KB Output is correct
49 Correct 3 ms 1492 KB Output is correct
50 Correct 1 ms 852 KB Output is correct