You are given two integers n and k. Your task is to find if n can be represented as a sum of k distinct positive odd (not divisible by 2) integers or not.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 10^5) — the number of test cases.

The next t lines describe test cases. The only line of the test case contains two integers n and k (1 ≤ n, k ≤ 10^7).

Output

For each test case, print the answer — "YES" (without quotes) if n can be represented as a sum of k distinct positive odd (not divisible by 2) integers and "NO" otherwise.

Example

Input


6
3 1
4 2
10 3
10 2
16 4
16 5


Output


YES
YES
NO
YES
YES
NO

Note

In the first test case, you can represent 3 as 3.

In the second test case, the only way to represent 4 is 1+3.

In the third test case, you cannot represent 10 as the sum of three distinct positive odd integers.

In the fourth test case, you can represent 10 as 3+7, for example.

In the fifth test case, you can represent 16 as 1+3+5+7.

In the sixth test case, you cannot represent 16 as the sum of five distinct positive odd integers.

import java.util.*;
import java.io.*;

public class SumofOddIntegers {

	public static void main(String[] args) throws IOException, FileNotFoundException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		//BufferedReader in = new BufferedReader(new FileReader("SumofOddIntegers.in"));
		// INPUT //

		long t = Integer.parseInt(in.readLine());  
		for (long i = 0; i < t; i++) {
			StringTokenizer st = new StringTokenizer(in.readLine());
			
			long n = Integer.parseInt(st.nextToken()); 
			long k = Integer.parseInt(st.nextToken());  
			
			if ((n-k) % 2 == 0 && ((n-k)/2) >= (k*(k-1)/2)) {
				System.out.println("YES");
			}
			else System.out.println("NO");

		}
		in.close();
	}
}

/*

for (int i = 0; i < t; i++) {
	StringTokenizer st = new StringTokenizer(in.readLine());
	
	int n = Integer.parseInt(st.nextToken()); 
	int k = Integer.parseInt(st.nextToken());  
	
	if ((n-k) % 2 == 0 && ((n-k)/2) >= (k*(k-1)/2)) {
		System.out.println("YES");
	}
	else System.out.println("NO");

}

*/

/*

for (int i = 0; i < t; i++) {
	StringTokenizer st = new StringTokenizer(in.readLine());
	
	int n = Integer.parseInt(st.nextToken()); 
	int k = Integer.parseInt(st.nextToken());
	
	if ((n - (k-1)*(k-1)) % 2 == 1 && (n - (k-1)*(k-1) + 1) / 2 > k-1) System.out.println("YES");
	else System.out.println("NO");	
}
*/