A. Reading Books
time limit per test
1 second
memory limit per test
128 megabytes
input
standard input
output
standard output

O–O loves to read books everyday.

He has $$$n$$$ days and $$$m$$$ books. In the $$$i$$$-th day, O–O reads $$$a_i$$$ pages. The array $$$b$$$ represents the number of pages in books.

In the $$$i$$$-th day, he wants to know the maximum number of books he already finished.

Input

The first line contains a single integer $$$t$$$ $$$(1 \le t \le 10^5)$$$ — the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers $$$n$$$ and $$$m$$$ $$$(1 \le n , m \le 2 ⋅ 10^5)$$$ — the length of the array $$$a$$$ and $$$b$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1,a_2 \dots a_n$$$ $$$(1 \le a_i \le 10^9)$$$.

The third line of each test case contains $$$m$$$ integers $$$b_1,b_2 \dots b_m$$$ $$$(1 \le b_i \le 10^9)$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 ⋅ 10^5$$$.

It is guaranteed that the sum of $$$m$$$ over all test cases does not exceed $$$2 ⋅ 10^5$$$.

Output

For each test case, output $$$n$$$ integers.

Example
Input
2
4 3
7 5 2 1
6 8 9
5 6
7 12 23 15 29
10 9 6 8 13 1
Output
1 1 2 2 
2 3 5 6 6