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.
 ... Can you provide a Python code to find any array a_1, a_2, …, a_n of integers such that all of the following conditions hold:?
assistant
#Here is Python code to find any array a_1, a_2, …, a_n of integers such that all of the following conditions hold: 
.

'''                      __      __        __                  __    __        __  __       
                      /  |    /  |      /  |                /  |  /  |     /   |/| |      
  _______   ______   _$$ |_   $$ |____  $$ |____    ______  $$/   _$$ |_    $$/ |$$ |   __ 
 /       | /       / $$   |  $$         $$        /         /  | / $$   |   /  |$$ |  /  |
/$$$$$$$/ /$$$$$$  |$$$$$$/   $$$$$$$  |$$$$$$$  |/$$$$$$  |$$ | $$$$$$/   $$  |$$ |_/$$/ 
$$        $$    $$ |  $$ | __ $$ |  $$ |$$ |  $$ |$$ |  $$/ $$ |  $$ | __  $$  |$$   $$<  
 $$$$$$  |$$$$$$$$/   $$ |/  |$$ |  $$ |$$ |  $$ |$$ |      $$ |  $$ |/  | $$  |$$$$$$  \
/     $$/ $$       |  $$  $$/ $$ |  $$ |$$ |  $$ |$$ |      $$ |  $$  $$/  $$  |$$ | $$  |
$$$$$$$/   $$$$$$$/    $$$$/  $$/   $$/ $$/   $$/ $$/       $$/    $$$$/   $$/ |$$/   $$/ 
                                                                                        
'''                                                                                     
from __future__ import division, print_function

import os
import sys
from io import BytesIO, IOBase

if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from future_builtins import ascii, filter, hex, map, oct, zip

def main():
    pass

# region fastio

BUFSIZE = 8192

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
       ...