oj.uz

Submission #623411

# Submission time Handle Problem Language Result Execution time Memory
623411 2022-08-05T14:35:06 Z Arinoor Party (INOI20_party) C++17
40 / 100
 3000 ms 3284 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(h == lg and !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 15 ms 468 KB Output is correct
12 Correct 17 ms 468 KB Output is correct
13 Correct 17 ms 472 KB Output is correct
14 Correct 16 ms 476 KB Output is correct
15 Correct 14 ms 472 KB Output is correct
16 Correct 15 ms 464 KB Output is correct
17 Correct 14 ms 468 KB Output is correct
18 Correct 19 ms 468 KB Output is correct
19 Correct 16 ms 472 KB Output is correct
20 Correct 15 ms 456 KB Output is correct

Subtask #2
0 / 23.0

# Verdict Execution time Memory Grader output
1 Correct 224 ms 3188 KB Output is correct
2 Correct 254 ms 3060 KB Output is correct
3 Correct 232 ms 3116 KB Output is correct
4 Correct 195 ms 3100 KB Output is correct
5 Correct 250 ms 3276 KB Output is correct
6 Correct 227 ms 3148 KB Output is correct
7 Correct 208 ms 3176 KB Output is correct
8 Correct 232 ms 3192 KB Output is correct
9 Correct 219 ms 3256 KB Output is correct
10 Correct 237 ms 3120 KB Output is correct
11 Execution timed out 3095 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 257 ms 3084 KB Output is correct
2 Correct 241 ms 3136 KB Output is correct
3 Correct 208 ms 3184 KB Output is correct
4 Correct 219 ms 3284 KB Output is correct
5 Correct 250 ms 3248 KB Output is correct
6 Correct 239 ms 3192 KB Output is correct
7 Correct 241 ms 3132 KB Output is correct
8 Correct 260 ms 3248 KB Output is correct
9 Correct 227 ms 3176 KB Output is correct
10 Correct 243 ms 3184 KB Output is correct
11 Correct 856 ms 3196 KB Output is correct
12 Correct 890 ms 3276 KB Output is correct
13 Correct 881 ms 3184 KB Output is correct
14 Correct 886 ms 3180 KB Output is correct
15 Correct 876 ms 3192 KB Output is correct
16 Correct 908 ms 3180 KB Output is correct
17 Correct 861 ms 3180 KB Output is correct
18 Correct 904 ms 3180 KB Output is correct
19 Correct 920 ms 3188 KB Output is correct
20 Correct 893 ms 3180 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 15 ms 468 KB Output is correct
12 Correct 17 ms 468 KB Output is correct
13 Correct 17 ms 472 KB Output is correct
14 Correct 16 ms 476 KB Output is correct
15 Correct 14 ms 472 KB Output is correct
16 Correct 15 ms 464 KB Output is correct
17 Correct 14 ms 468 KB Output is correct
18 Correct 19 ms 468 KB Output is correct
19 Correct 16 ms 472 KB Output is correct
20 Correct 15 ms 456 KB Output is correct
21 Correct 224 ms 3188 KB Output is correct
22 Correct 254 ms 3060 KB Output is correct
23 Correct 232 ms 3116 KB Output is correct
24 Correct 195 ms 3100 KB Output is correct
25 Correct 250 ms 3276 KB Output is correct
26 Correct 227 ms 3148 KB Output is correct
27 Correct 208 ms 3176 KB Output is correct
28 Correct 232 ms 3192 KB Output is correct
29 Correct 219 ms 3256 KB Output is correct
30 Correct 237 ms 3120 KB Output is correct
31 Execution timed out 3095 ms 3184 KB Time limit exceeded
32 Halted 0 ms 0 KB -