oj.uz

Submission #623408

# Submission time Handle Problem Language Result Execution time Memory
623408 2022-08-05T14:31:53 Z Arinoor Party (INOI20_party) C++17
40 / 100
 3000 ms 3272 KB 
#include <bits/stdc++.h>
using namespace std;

#define ios				ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0)
#define pb				push_back
#define mp				make_pair
#define fi				first
#define se				second
#define all(x)			x.begin(), x.end()
#define bug(x)			cout << #x << " : " << x << '\n'

typedef long long ll;
typedef pair<int, int> pii;

const int maxn = 60;
const int mod = 1e9 + 7;
const int inf = 1e9 + 10;

ll n;
int dp[maxn << 1][maxn][maxn], pd[maxn << 1][maxn][maxn], pw[maxn], lg;

inline int add(int a, int b){
	int c = a + b;
	if(c >= mod) c -= mod;
	return c;
}

inline int neg(int a, int b){
	int c = a - b;
	if(c < 0) c += mod;
	return c;
}

inline int mul(int a, int b){
	return 1ll * a * b % mod;
}

inline int pwr(int a, int b){
	int res = 1;
	for(; b; b >>= 1, a = mul(a, a)) if(b & 1) res = mul(res, a);
	return res;
}

inline bool check(int h, int H){
	if(h > lg)
		return false;
	if(h < lg or H == lg)
		return true;
	return n >> (lg - (H + 1)) & 1;
}

inline int get_cnt(int h, int H){
	if(h > lg)
		return 0;
	if(h < lg or H == lg)
		return pw[max(0, h - H - 1)];
	if(!check(h, H))
		return 0;
	return pw[h - H - 1];
}

int main(){
	ios;
	pw[0] = 1;
	for(int i = 1; i < maxn; i ++)
		pw[i] = add(pw[i - 1], pw[i - 1]);
	int q; cin >> q;
	while(q--){
		cin >> n;
		if(n == 1){
			cout << "0\n";
			continue;
		}
		lg = 63 - __builtin_clzll(n);
		int inv = pwr(2, mod - 2);
		for(int h = 0; h <= lg; h ++){
			for(int H = 0; H <= h; H ++){
				dp[0][h][H] = pd[0][h][H] = dp[1][h][H] = pd[1][h][H] = 1;
				if(check(h, H)){
					dp[0][h][H] = 2;
					pd[0][h][H] = inv;
					int cnt = 0;
					if(H < h){
						cnt = 2 * check(h + 1, H) + 1;
					}
					else{
						cnt = check(h + 1, H) + check(h + 1, H + 1) + (h > 0);
					}
					dp[1][h][H] = pwr(2, cnt);
					pd[1][h][H] = pwr(inv, cnt);
				}
			}
		}
		for(int l = 2; l <= lg * 2; l ++){
			for(int h = max(0, l - lg); h <= lg; h ++){
				for(int H = 0; H <= h; H ++){
					int &r1 = dp[l][h][H];
					int &r2 = pd[l][h][H];
					r1 = r2 = 1;
					if(!check(h, H))
						continue;
					int cnt;
					if(H < h){
						if(h < lg){
							r1 = mul(dp[l - 1][h + 1][H], dp[l - 1][h + 1][H]);
							r2 = mul(pd[l - 1][h + 1][H], pd[l - 1][h + 1][H]);
						}
						r1 = mul(r1, dp[l - 1][h - 1][H]);
						r2 = mul(r2, pd[l - 1][h - 1][H]);
						cnt = 2 * check(h + 1, H) + 1;
					}
					else{
						if(h < lg){
							r1 = mul(dp[l - 1][h + 1][H], dp[l - 1][h + 1][H + 1]);
							r2 = mul(pd[l - 1][h + 1][H], pd[l - 1][h + 1][H + 1]);
						}
						if(h){
							r1 = mul(r1, dp[l - 1][h - 1][H - 1]);
							r2 = mul(r2, pd[l - 1][h - 1][H - 1]);
						}
						cnt = check(h + 1, H + 1) + check(h + 1, H) + (h > 0);
					}
					if(l > 2)
						cnt --;
					if(cnt == 2){
						r1 = mul(r1, mul(pd[l - 2][h][H], pd[l - 2][h][H]));
						r2 = mul(r2, mul(dp[l - 2][h][H], dp[l - 2][h][H]));
					}
					else if(cnt == 1){
						r1 = mul(r1, pd[l - 2][h][H]);
						r2 = mul(r2, dp[l - 2][h][H]);
					}
					else if(cnt == 3){
						r1 = mul(r1, pwr(pd[l - 2][h][H], 3));
						r2 = mul(r2, pwr(dp[l - 2][h][H], 3));
					}
				}
			}
		}
		int ans = 0;
		int tot = pwr(2, n % (mod - 1));
		for(int h = 0; h <= lg; h ++){
			for(int H = 0; H <= h; H ++){
				int res = 0;
				int p = tot;
				for(int l = 0; l <= lg + h; l ++){
					p = mul(p, pd[l][h][H]);
					int cnt = mul(neg(dp[l][h][H], 1), p);
					res = add(res, mul(cnt, l));
				}
				ans = add(ans, mul(res, get_cnt(h, H)));
			}
		}
		inv = pwr(neg(tot, 1), mod - 2);
		cout << mul(ans, inv) << '\n';
	}
}

Subtask #1
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 468 KB Output is correct
6 Correct 1 ms 468 KB Output is correct
7 Correct 1 ms 468 KB Output is correct
8 Correct 1 ms 468 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 340 KB Output is correct
11 Correct 18 ms 472 KB Output is correct
12 Correct 15 ms 460 KB Output is correct
13 Correct 15 ms 468 KB Output is correct
14 Correct 16 ms 476 KB Output is correct
15 Correct 14 ms 468 KB Output is correct
16 Correct 15 ms 472 KB Output is correct
17 Correct 16 ms 468 KB Output is correct
18 Correct 15 ms 468 KB Output is correct
19 Correct 14 ms 472 KB Output is correct
20 Correct 17 ms 460 KB Output is correct

Subtask #2
0 / 23.0

# Verdict Execution time Memory Grader output
1 Correct 223 ms 3192 KB Output is correct
2 Correct 262 ms 3184 KB Output is correct
3 Correct 229 ms 3176 KB Output is correct
4 Correct 201 ms 3072 KB Output is correct
5 Correct 256 ms 3188 KB Output is correct
6 Correct 237 ms 3180 KB Output is correct
7 Correct 230 ms 3184 KB Output is correct
8 Correct 218 ms 3180 KB Output is correct
9 Correct 243 ms 3184 KB Output is correct
10 Correct 246 ms 3120 KB Output is correct
11 Execution timed out 3030 ms 3184 KB Time limit exceeded
12 Halted 0 ms 0 KB -

Subtask #3
33.0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 249 ms 3176 KB Output is correct
2 Correct 252 ms 3196 KB Output is correct
3 Correct 208 ms 3156 KB Output is correct
4 Correct 215 ms 3180 KB Output is correct
5 Correct 252 ms 3244 KB Output is correct
6 Correct 263 ms 3272 KB Output is correct
7 Correct 233 ms 3136 KB Output is correct
8 Correct 264 ms 3244 KB Output is correct
9 Correct 228 ms 3188 KB Output is correct
10 Correct 245 ms 3144 KB Output is correct
11 Correct 885 ms 3184 KB Output is correct
12 Correct 881 ms 3184 KB Output is correct
13 Correct 894 ms 3196 KB Output is correct
14 Correct 861 ms 3184 KB Output is correct
15 Correct 881 ms 3184 KB Output is correct
16 Correct 864 ms 3188 KB Output is correct
17 Correct 879 ms 3184 KB Output is correct
18 Correct 856 ms 3188 KB Output is correct
19 Correct 860 ms 3184 KB Output is correct
20 Correct 891 ms 3188 KB Output is correct

Subtask #4
0 / 37.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 468 KB Output is correct
6 Correct 1 ms 468 KB Output is correct
7 Correct 1 ms 468 KB Output is correct
8 Correct 1 ms 468 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 340 KB Output is correct
11 Correct 18 ms 472 KB Output is correct
12 Correct 15 ms 460 KB Output is correct
13 Correct 15 ms 468 KB Output is correct
14 Correct 16 ms 476 KB Output is correct
15 Correct 14 ms 468 KB Output is correct
16 Correct 15 ms 472 KB Output is correct
17 Correct 16 ms 468 KB Output is correct
18 Correct 15 ms 468 KB Output is correct
19 Correct 14 ms 472 KB Output is correct
20 Correct 17 ms 460 KB Output is correct
21 Correct 223 ms 3192 KB Output is correct
22 Correct 262 ms 3184 KB Output is correct
23 Correct 229 ms 3176 KB Output is correct
24 Correct 201 ms 3072 KB Output is correct
25 Correct 256 ms 3188 KB Output is correct
26 Correct 237 ms 3180 KB Output is correct
27 Correct 230 ms 3184 KB Output is correct
28 Correct 218 ms 3180 KB Output is correct
29 Correct 243 ms 3184 KB Output is correct
30 Correct 246 ms 3120 KB Output is correct
31 Execution timed out 3030 ms 3184 KB Time limit exceeded
32 Halted 0 ms 0 KB -