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ID题目提交者结果用时内存语言文件大小提交时间测评时间
#93978#6137. Sub-cycle GraphksunhokimAC ✓1331ms4960kbC++201.6kb2023-04-04 12:17:572023-04-04 12:18:01

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-04-04 12:18:01]
  • 评测
  • 测评结果:AC
  • 用时:1331ms
  • 内存:4960kb
  • [2023-04-04 12:17:57]
  • 提交

answer

#include <iostream>
using namespace std;
#define MOD 1000000007
#define MAXN 100005

long long fastExp(long long base, long long exp)
{
    long long res = 1;
    while (exp > 0)
    {
        if (exp & 1)
            res = res * base % MOD;
        base = base * base % MOD;
        exp >>= 1;
    }
    return res;
}

long long modInverse(long long num)
{
    return fastExp(num, MOD - 2);
}

long long fact[MAXN], inv[MAXN];

long long choose(int a, int b)
{
    if (b == 0)
        return 1;
    return (fact[a] * inv[b] % MOD) * inv[a - b] % MOD;
}

long long solve()
{
    long long n, m;
    cin >> n >> m;
    if (m > n)
        return 0;
    if (m == n)
        return fact[n - 1] * modInverse(2) % MOD;
    if (m == 0)
        return 1;

    long long ans = 0;
    for (int i = 1; i <= min(m, n - m); i++)
    {
        long long cur = fact[n] * inv[n - m - i] % MOD;
        //cout << "a" << cur << endl;
        cur = cur * modInverse(fastExp(2, i)) % MOD;
        cur = cur * inv[i] % MOD;
        //cout << "b" << cur << endl;
        cur = cur * choose(m - 1, i - 1) % MOD;
        //cout << "c" << m - 1 << " " << i - 1 << endl;
        ans += cur;
        if (ans >= MOD)
            ans -= MOD;
        //cout << "cur: " << cur << endl;
    }
    return ans;
}

int main()
{
    fact[0] = 1;
    inv[0] = 1;
    for (int i = 1; i < MAXN; i++)
    {
        fact[i] = i * fact[i - 1] % MOD;
        inv[i] = modInverse(fact[i]);
    }

    int t;
    cin >> t;
    while (t--)
    {
        cout << solve() << endl;
    }
}

详细

Test #1:

score: 100
Accepted
time: 13ms
memory: 4960kb

input:

3
4 2
4 3
5 3

output:

15
12
90

result:

ok 3 number(s): "15 12 90"

Test #2:

score: 0
Accepted
time: 1331ms
memory: 4888kb

input:

17446
3 0
3 1
3 2
3 3
4 0
4 1
4 2
4 3
4 4
5 0
5 1
5 2
5 3
5 4
5 5
6 0
6 1
6 2
6 3
6 4
6 5
6 6
7 0
7 1
7 2
7 3
7 4
7 5
7 6
7 7
8 0
8 1
8 2
8 3
8 4
8 5
8 6
8 7
8 8
9 0
9 1
9 2
9 3
9 4
9 5
9 6
9 7
9 8
9 9
10 0
10 1
10 2
10 3
10 4
10 5
10 6
10 7
10 8
10 9
10 10
11 0
11 1
11 2
11 3
11 4
11 5
11 6
11 7
11...

output:

1
3
3
1
1
6
15
12
3
1
10
45
90
60
12
1
15
105
375
630
360
60
1
21
210
1155
3465
5040
2520
360
1
28
378
2940
13545
35280
45360
20160
2520
1
36
630
6552
42525
170100
393120
453600
181440
20160
1
45
990
13230
114345
643545
2286900
4762800
4989600
1814400
181440
1
55
1485
24750
273735
2047815
10239075
3...

result:

ok 17446 numbers