#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define endl "\n"
using namespace std;
using namespace __gnu_pbds;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
template<class T> using ordered_set = tree<T, null_type, less_equal<T>, rb_tree_tag, tree_order_statistics_node_update>;
const ll mod = 1e9 + 7, N = 1e6 + 5;
ll pw[N], n;
ll freq[120];
void precomp()
{
pw[0] = 1;
for (ll i = 1; i < N; i++) pw[i] = pw[i - 1] * 2 % mod;
}
ll binpow(ll n, ll p)
{
ll ans = 1;
while (p)
{
ans = (p & 1 ? (ans * n) % mod : ans);
n = (n * n) % mod;
p >>= 1;
}
return ans;
}
ll pww(ll p)
{
if (p < N) return pw[p];
if (p & 1)
{
p = pww(p >> 1);
return p * p * 2 % mod;
}
p = pww(p >> 1);
return p * p % mod;
}
ll inv(ll x)
{
return binpow(x, mod - 2);
}
void dfs(ll v, ll par = 0, ll depth = 0)
{
freq[depth]++;
for (ll to : {v >> 1, v * 2, v * 2 + 1}) if (to != par and to <= n and to >= 1) dfs(to, v, depth + 1);
}
void solve()
{
cin >> n;
if (n <= 200){
ll ans = 0;
for (ll i = 1; i <= n; i++)
{
for (ll j = 0; j < 20; j++) freq[j] = 0;
dfs(i);
ll cur = 0;
for (ll j = 19; j >= 0; j--)
ans = (ans + binpow(2, cur) * (binpow(2, freq[j]) - 1) % mod * j % mod) % mod, cur += freq[j];
}
ans = ans * inv(binpow(2, n) - 1 + mod) % mod;
cout << ans << endl;
}
else
{
ll ans = 0, lg = __lg(n);
ll freq[120];
for (ll i = 0; i <= lg; i++)
{
ll res = 0;
for (ll j = 0; j < 120; j++) freq[j] = 0;
for (ll j = 1; j <= i; j++){
freq[j]++;
for (ll x = 1; i - j + x <= lg; x++) freq[j + x] += (1ll << (x - 1));
}
for (ll x = 1; x + i <= lg; x++) freq[x] += (1ll << x);
ll cur = 0;
for (ll j = 119; j >= 0; j--)
res = (res + pww(cur) * (pww(freq[j]) - 1) % mod * j % mod) % mod, cur += freq[j];
ans = (ans + binpow(2, i) * res % mod) % mod;
}
ans = ans * inv(binpow(2, n) - 1 + mod) % mod;
cout << ans << endl;
}
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
ll t = 1;
// precomp();
cin >> t;
for (ll cs = 1; cs <= t; cs++)
solve();
// cerr << "\nTime elapsed: " << clock() * 1000.0 / CLOCKS_PER_SEC << " ms\n";
}
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
4 ms |
348 KB |
Output is correct |
2 |
Correct |
6 ms |
348 KB |
Output is correct |
3 |
Correct |
5 ms |
472 KB |
Output is correct |
4 |
Correct |
4 ms |
348 KB |
Output is correct |
5 |
Correct |
6 ms |
348 KB |
Output is correct |
6 |
Correct |
5 ms |
468 KB |
Output is correct |
7 |
Correct |
6 ms |
348 KB |
Output is correct |
8 |
Correct |
6 ms |
348 KB |
Output is correct |
9 |
Correct |
5 ms |
348 KB |
Output is correct |
10 |
Correct |
9 ms |
476 KB |
Output is correct |
11 |
Correct |
268 ms |
604 KB |
Output is correct |
12 |
Correct |
256 ms |
472 KB |
Output is correct |
13 |
Correct |
290 ms |
344 KB |
Output is correct |
14 |
Correct |
235 ms |
344 KB |
Output is correct |
15 |
Correct |
267 ms |
456 KB |
Output is correct |
16 |
Correct |
237 ms |
344 KB |
Output is correct |
17 |
Correct |
159 ms |
468 KB |
Output is correct |
18 |
Correct |
148 ms |
344 KB |
Output is correct |
19 |
Correct |
153 ms |
348 KB |
Output is correct |
20 |
Correct |
151 ms |
476 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Incorrect |
61 ms |
348 KB |
Output isn't correct |
2 |
Halted |
0 ms |
0 KB |
- |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Incorrect |
59 ms |
344 KB |
Output isn't correct |
2 |
Halted |
0 ms |
0 KB |
- |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
4 ms |
348 KB |
Output is correct |
2 |
Correct |
6 ms |
348 KB |
Output is correct |
3 |
Correct |
5 ms |
472 KB |
Output is correct |
4 |
Correct |
4 ms |
348 KB |
Output is correct |
5 |
Correct |
6 ms |
348 KB |
Output is correct |
6 |
Correct |
5 ms |
468 KB |
Output is correct |
7 |
Correct |
6 ms |
348 KB |
Output is correct |
8 |
Correct |
6 ms |
348 KB |
Output is correct |
9 |
Correct |
5 ms |
348 KB |
Output is correct |
10 |
Correct |
9 ms |
476 KB |
Output is correct |
11 |
Correct |
268 ms |
604 KB |
Output is correct |
12 |
Correct |
256 ms |
472 KB |
Output is correct |
13 |
Correct |
290 ms |
344 KB |
Output is correct |
14 |
Correct |
235 ms |
344 KB |
Output is correct |
15 |
Correct |
267 ms |
456 KB |
Output is correct |
16 |
Correct |
237 ms |
344 KB |
Output is correct |
17 |
Correct |
159 ms |
468 KB |
Output is correct |
18 |
Correct |
148 ms |
344 KB |
Output is correct |
19 |
Correct |
153 ms |
348 KB |
Output is correct |
20 |
Correct |
151 ms |
476 KB |
Output is correct |
21 |
Incorrect |
61 ms |
348 KB |
Output isn't correct |
22 |
Halted |
0 ms |
0 KB |
- |