CQXYM Count Permutations codeforces solution

CQXYM Count Permutations codeforces solution

CQXYM is counting permutations length of 2n2n.

A permutation is an array consisting of nn distinct integers from 11 to nn in arbitrary order. For example, [2,3,1,5,4][2,3,1,5,4] is a permutation, but [1,2,2][1,2,2] is not a permutation (22 appears twice in the array) and [1,3,4][1,3,4] is also not a permutation (n=3n=3 but there is 44 in the array).

A permutation pp(length of 2n2n) will be counted only if the number of ii satisfying pi<pi+1pi<pi+1 is no less than nn. For example:

  • Permutation [1,2,3,4][1,2,3,4] will count, because the number of such ii that pi<pi+1pi<pi+1 equals 33 (i=1i=1i=2i=2i=3i=3).
  • Permutation [3,2,1,4][3,2,1,4] won’t count, because the number of such ii that pi<pi+1pi<pi+1 equals 11 (i=3i=3).

CQXYM wants you to help him to count the number of such permutations modulo 10000000071000000007 (109+7109+7).

In addition, modulo operation is to get the remainder. For example:

  • 7mod3=17mod3=1, because 7=32+17=3⋅2+1,
  • 15mod4=315mod4=3, because 15=43+315=4⋅3+3.

CQXYM Count Permutations codeforces solution

Input

The input consists of multiple test cases.

The first line contains an integer t(t1)t(t≥1) — the number of test cases. The description of the test cases follows.

Only one line of each test case contains an integer n(1n105)n(1≤n≤105).

It is guaranteed that the sum of nn over all test cases does not exceed 105105

Output

For each test case, print the answer in a single line.

CQXYM Count Permutations codeforces solution

Example

input

Copy
4
1
2
9
91234

output

Copy
1
12
830455698
890287984

CQXYM Count Permutations codeforces solution

Note

n=1n=1, there is only one permutation that satisfies the condition: [1,2].[1,2].

In permutation [1,2][1,2]p1<p2p1<p2, and there is one i=1i=1 satisfy the condition. Since 1n1≥n, this permutation should be counted. In permutation [2,1][2,1]p1>p2p1>p2. Because 0<n0<n, this permutation should not be counted.

n=2n=2, there are 1212 permutations: [1,2,3,4],[1,2,4,3],[1,3,2,4],[1,3,4,2],[1,4,2,3],[2,1,3,4],[2,3,1,4],[2,3,4,1],[2,4,1,3],[3,1,2,4],[3,4,1,2],[4,1,2,3].[1,2,3,4],[1,2,4,3],[1,3,2,4],[1,3,4,2],[1,4,2,3],[2,1,3,4],[2,3,1,4],[2,3,4,1],[2,4,1,3],[3,1,2,4],[3,4,1,2],[4,1,2,3].

CQXYM Count Permutations solution codeforces

Solution


int n;
      cin>>n;
      ll ans=1;
      ll mod=1e9+7;

      for(int i=2*n;i>=3;i--){
        ans=(ans*i)%mod;;
      }
      ans=ans%mod;

      cout<<ans<<"\n";
 

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