B. Wara B3d Wara B3d
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Your task is to determine whether it is possible to find exactly $$$m$$$ consecutive positive integers such that their total sum is exactly equal to $$$n$$$.

A sequence of numbers is considered strictly consecutive positive integers if it consists of integers greater than zero that follow each other continuously, with each subsequent number being exactly $$$1$$$ greater than the previous one. For example, $$$4, 5, 6$$$ are three consecutive positive integers, while $$$2, 4, 6$$$ (has gaps) and $$$-1, 0, 1$$$ (contains non-positive numbers) are not

Input

The first line of the input contains a single integer $$$t$$$ ($$$1 \le t \le 10^5$$$) — the number of test cases.Each of the next $$$t$$$ lines contains two space-separated integers $$$n$$$ and $$$m$$$ ($$$1 \le n \le 10^{9},1 \le m \le 10^{9}$$$) — the target sum and the required number of consecutive positive integers, respectively.

Output

For each test case, output YES if it is possible to form the sum $$$n$$$ using exactly $$$m$$$ consecutive positive integers. Otherwise, output NO.You can output the answer in any case (for example, the strings "yEs", "yes", "Yes", and "YES" will all be recognized as a positive answer).

Example
Input
1
18 3
Output
YES
Note

for the given testcase the three consecutive integers are: 5,6,7