CQXYM Count Permutations solution codeforces

CQXYM Count Permutations solution codeforces

CQXYM is counting permutations length of 2n.

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

CQXYM Count Permutations solution codeforces

A permutation p(length of 2n) will be counted only if the number of i satisfying pi<pi+1 is no less than n. For example:

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

CQXYM wants you to help him to count the number of such permutations modulo 1000000007 (109+7).

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

  • 7mod3=1, because 7=32+1,
  • 15mod4=3, because 15=43+3.

Input CQXYM Count Permutations solution codeforces

The input consists of multiple test cases.

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

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

It is guaranteed that the sum of n over all test cases does not exceed 105

Output CQXYM Count Permutations solution codeforces

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

Example
input

Copy
4
1
2
9
91234

output CQXYM Count Permutations solution codeforces

Copy

1
12
830455698
890287984

Note CQXYM Count Permutations solution codeforces

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

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

n=2, there are 12 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].

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