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Submission #897736

# Submission time Handle Problem Language Result Execution time Memory
897736 2024-01-03T15:48:14 Z denniskim NoM (RMI21_nom) C++17
100 / 100
 139 ms 31824 KB 
#include <bits/stdc++.h>
#pragma GCC optimize ("O3")
#pragma GCC optimize ("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,avx,avx2")
 
using namespace std;
typedef long long ll;
typedef __int128 lll;
typedef long double ld;
typedef pair<ll, ll> pll;
typedef pair<ld, ld> pld;
#define MAX 9223372036854775807LL
#define MIN -9223372036854775807LL
#define INF 0x3f3f3f3f3f3f3f3f
#define fi first
#define se second
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); cout << fixed; cout.precision(10);
#define sp << " "
#define en << "\n"
#define compress(v) sort(v.begin(), v.end()), v.erase(unique(v.begin(), v.end()), v.end())
 
ll n, m;
ll ss = 1000000007;
ll ans;
ll cou[2010];
ll dp[9000010];
ll fac[5010] = {0, }, inv[5010] = {0, };
 
ll num(ll X, ll Y)
{
	return X * (m + 1) + Y;
}
 
ll power(ll xx, ll yy)
{
    ll ret = 1;
     
    while(yy > 0)
    {
        if(yy % 2)
            ret = (ret * xx) % ss;
        xx = (xx * xx) % ss;
        yy /= 2;
    }
     
    return ret;
}
 
ll C(ll xx, ll yy)
{
	if(xx < yy)
		return 0;
	
    if(xx == yy || !yy)
        return 1;
    
    long long r = (fac[xx] * inv[xx - yy]) % ss;
    r = (r * inv[yy]) % ss;
    return r;
}
 
void init(void)
{
	fac[0] = 1;
    fac[1] = 1;
     
    for(ll i = 2 ; i <= 4500 ; i++)
        fac[i] = (fac[i - 1] * i) % ss;
     
    inv[4500] = power(fac[4500], ss - 2);
    
    for(ll i = 4499 ; i >= 0 ; i--)
        inv[i] = (inv[i + 1] * (i + 1)) % ss;
}
 
int main(void)
{
	fastio
	
	cin >> n >> m;
	
	init();
	
	ll siz = n * 2;
	
	ans = fac[siz];
	
	for(ll i = 1 ; i <= siz ; ++i)
	{
		ll gap = i % m;
		
		if(gap == 0)
			gap = m;
		
		cou[gap]++;
	}
	
	for(ll i = 0 ; i <= m ; ++i)
		dp[num(0, i)] = 1;
	
	for(ll i = 1 ; i <= n ; ++i)
	{
		for(ll j = 1 ; j <= m ; ++j)
		{
			ll X = cou[j];
			
			for(ll k = 1 ; k * 2 <= X && k <= i ; ++k)
            {
				dp[num(i, j)] = (dp[num(i, j)] + dp[num(i - k, j - 1)] * C(X, k * 2) % ss * fac[k * 2] % ss * C(i, k) % ss);
              	while(abs(dp[num(i, j)]) > ss)
                {
                    if(dp[num(i, j)] < 0)
                        dp[num(i, j)] += ss;
                    else
                        dp[num(i, j)] -= ss;
                }
            }
		}
		
		for(ll j = 1 ; j <= m ; ++j)
        {
			dp[num(i, j)] = (dp[num(i, j)] + dp[num(i, j - 1)]);
          
          	while(abs(dp[num(i, j)]) > ss)
			{
				if(dp[num(i, j)] < 0)
					dp[num(i, j)] += ss;
				else
					dp[num(i, j)] -= ss;
			}
        }
	}
	
	for(ll i = 1 ; i <= n ; ++i)
	{
		ll gap = dp[num(i, m)] * C(n, i) % ss * fac[n * 2 - i * 2] % ss;
		
		if(i & 1)
			ans = (ans - gap);
		else
			ans = (ans + gap);
      
      	while(abs(ans) > ss)
        {
          if(ans < 0)
            ans += ss;
          else
            ans -= ss;
        }
	}
	
	ans = (ans + ss) % ss;
	
	cout << ans;
	return 0;
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 1 ms 520 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 1 ms 544 KB Output is correct

Subtask #3
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 1 ms 520 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 1 ms 544 KB Output is correct
20 Correct 2 ms 348 KB Output is correct
21 Correct 1 ms 604 KB Output is correct
22 Correct 3 ms 860 KB Output is correct
23 Correct 3 ms 348 KB Output is correct
24 Correct 4 ms 856 KB Output is correct
25 Correct 3 ms 860 KB Output is correct
26 Correct 4 ms 344 KB Output is correct
27 Correct 3 ms 1116 KB Output is correct

Subtask #4
18.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 1 ms 520 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 1 ms 544 KB Output is correct
20 Correct 2 ms 348 KB Output is correct
21 Correct 1 ms 604 KB Output is correct
22 Correct 3 ms 860 KB Output is correct
23 Correct 3 ms 348 KB Output is correct
24 Correct 4 ms 856 KB Output is correct
25 Correct 3 ms 860 KB Output is correct
26 Correct 4 ms 344 KB Output is correct
27 Correct 3 ms 1116 KB Output is correct
28 Correct 21 ms 596 KB Output is correct
29 Correct 16 ms 2172 KB Output is correct
30 Correct 13 ms 3420 KB Output is correct
31 Correct 21 ms 576 KB Output is correct
32 Correct 18 ms 2140 KB Output is correct
33 Correct 16 ms 3932 KB Output is correct
34 Correct 28 ms 6852 KB Output is correct

Subtask #5
48.0 / 48.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 1 ms 520 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 1 ms 544 KB Output is correct
20 Correct 2 ms 348 KB Output is correct
21 Correct 1 ms 604 KB Output is correct
22 Correct 3 ms 860 KB Output is correct
23 Correct 3 ms 348 KB Output is correct
24 Correct 4 ms 856 KB Output is correct
25 Correct 3 ms 860 KB Output is correct
26 Correct 4 ms 344 KB Output is correct
27 Correct 3 ms 1116 KB Output is correct
28 Correct 21 ms 596 KB Output is correct
29 Correct 16 ms 2172 KB Output is correct
30 Correct 13 ms 3420 KB Output is correct
31 Correct 21 ms 576 KB Output is correct
32 Correct 18 ms 2140 KB Output is correct
33 Correct 16 ms 3932 KB Output is correct
34 Correct 28 ms 6852 KB Output is correct
35 Correct 139 ms 556 KB Output is correct
36 Correct 104 ms 23888 KB Output is correct
37 Correct 136 ms 1104 KB Output is correct
38 Correct 103 ms 11104 KB Output is correct
39 Correct 82 ms 19024 KB Output is correct
40 Correct 133 ms 31824 KB Output is correct