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).

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

  * Permutation [1, 2, 3, 4] will count, because the number of such i that p_i<p_{i+1} equals 3 (i = 1, i = 2, i = 3).
  * Permutation [3, 2, 1, 4] won't count, because the number of such i that p_i<p_{i+1} equals 1 (i = 3). 



CQXYM wants you to help him to count the number of such permutations modulo 1000000007 (10^9+7).

In addition, [modulo operation](https://en.wikipedia.org/wiki/Modulo_operation) is to get the remainder. For example:

  * 7 mod 3=1, because 7 = 3 ⋅ 2 + 1, 
  * 15 mod 4=3, because 15 = 4 ⋅ 3 + 3. 

Input

The input consists of multiple test cases. 

The first line contains an integer 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(1 ≤ n ≤ 10^5).

It is guaranteed that the sum of n over all test cases does not exceed 10^5

Output

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

Example

Input


4
1
2
9
91234


Output


1
12
830455698
890287984

Note

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

In permutation [1,2], p_1<p_2, and there is one i=1 satisfy the condition. Since 1 ≥ n, this permutation should be counted. In permutation [2,1], p_1>p_2. 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].
import sys
import os
from io import BytesIO

if sys.version_info[0] < 3:
    sys.stdin = BytesIO(os.read(0, os.fstat(0).st_size))

f = sys.stdin
if os.environ.get('USER') == "loic":
    f = open("data.in")

line = lambda: f.readline().strip('\r\n').split()

def write(w):
    sys.stdout.write(w)
    sys.stdout.write("\n")

def factorial_modulo(limit):
    fact = [1]
    for i in range(1, limit+1):
        fact.append(fact[-1] * i % M)
    return fact

def inv_modulo_all(limit):
    mod_inv = [0,1]
    for i in range(2, limit+1):
        mod_inv.append(M - (M // i) * mod_inv[M % i] % M)
    return mod_inv

def factorial_modulo_inverse(limit):
    mod_inv = inv_modulo_all(limit)
    fact_inv = [1,1]
    for i in range(2, limit+1):
        fact_inv.append(fact_inv[-1] * mod_inv[i] % M)
    return fact_inv

def solve():
    res = FACT[2*N] * FACT_INV[2]
    res %= M
    
    return str(res)

M = 10**9 + 7
Z = 200001
FACT = factorial_modulo(Z)

T = int(line()[0])
for test in range(1,T+1):
    N = int(line()[0])
    FACT_INV = factorial_modulo_inverse(2)
    
    write(solve())
    
f.close()