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.
#!/us
Write me a Python program to find any array a_1, a_2, …, a_n of integers such that all of the following conditions hold:?
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: 
.
r/bin/env python
from __future__ import division, print_function
import os
import sys
from io import BytesIO, IOBase
from collections import *
from bisect import *
from string import *
from itertools import * 
from statistics import *
from math import *
from heapq import heappush as push, heappop as pop
from re import *
from functools import cmp_to_key
from queue import *
mod  = int(1e9+7)
mod1 = 998244353
imax = float("inf")
imin = float("-inf")
true = True
false= False
N    = 10**5
vowels = "aeiou"
none = None
t3bit = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
inp  = lambda : input()
I    = lambda : int(inp())
M    = lambda : map(int,inp().split())
MS   = lambda : map(str,inp().split())
S    = lambda : list(MS())
L    = lambda : list(M())
test_case_run__ = false;
def case():global test_case_run__;test_case_run__ = true;
def exit():raise SystemExit
if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from future_builtins import ascii, filter, hex, map, oct, zip
#-------------------------------------------------------------------------------------------------------------------------------------

case()
def main():
    n=I()
    for i in range(n):
        print(1000+i,end= " ")
    print()

#-------------------------------------------------------------------------------------------------------------------------------------
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()
   ...