human
Given n, find any array a_1, a_2, …, a_n of integers such that all of the following conditions hold: 

  * 1 ≤ a_i ≤ 10^9 for every i from 1 to n.

  * a_1 < a_2 < … <a_n

  * For every i from 2 to n, a_i isn't divisible by a_{i-1}



It can be shown that such an array always exists under the constraints of the problem.

Input

The first line contains the number of test cases t (1 ≤ t ≤ 100). Description of the test cases follows.

The only line of each test case contains a single integer n (1 ≤ n ≤ 1000).

It is guaranteed that the sum of n over all test cases does not exceed 10^4.

Output

For each test case print n integers a_1, a_2, …, a_n — the array you found. If there are multiple arrays satisfying all the conditions, print any of them.

Example

Input

3
1
2
7

Output

1
2 3
111 1111 11111 111111 1111111 11111111 111111111

Note

In the first test case, array [1] satisfies all the conditions.

In the second test case, array [2, 3] satisfies all the conditions, as 2<3 and 3 is not divisible by 2.

In the third test case, array [111, 1111, 11111, 111111, 1111111, 11111111, 111111111] satisfies all the conditions, as it's increasing and a_i isn't divisible by a_{i-1} for any i from 2 to 7.
assistant
#Here is Python program to find any array a_1, a_2, …, a_n of integers such that all of the following conditions hold: 
.

from math import *
import sys
input = sys.stdin.readline

def inp():
    return(int(input()))
def inlt():
    return(list(map(int,input().split())))
def insr():
    s = input()
    return(list(s[:len(s) - 1]))
def invr():
    return(map(int,input().split()))

class Solution:
    def __init__(self):
        self.ans = 0
    def solve(self, a):
        x = []
        for i in range(2, a+2):
            x.append(i)
        return x

if __name__ == "__main__":
    sol = Solution()
    t =inp()
    k = t
    ans = []

    while t:
        x = inp()
        ans.append(sol.solve(x))
        t -= 1

    for i in range(k):
        for j in range(len(ans[i])):
            print(ans[i][j], end= " ")
        print(end="\n")