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 A
{
    static IO io = new IO();
	static int[] a;
    public static void main(String[] args)
    {
		int T = io.getInt();
		while(T-->0){
			long n = io.getInt();
			long k = io.getInt();
			
			if(n >= k*k && (k%2 == n%2))
				io.println("YES");
			else
				io.println("NO");
			
		}
		
		
        io.close();
    }
}



class IO extends PrintWriter {
	public IO() {
        super(new BufferedOutputStream(System.out));
        r = new BufferedReader(new InputStreamReader(System.in));
    }

    public IO(String fileName) {
        super(new BufferedOutputStream(System.out));
        try{
            r = new BufferedReader(new FileReader(fileName));
        } catch (FileNotFoundException e) {
            this.println("File Not Found");
        }
    }

    public boolean hasMoreTokens() {
        return peekToken() != null;
    }

    public int getInt() {
        return Integer.parseInt(nextToken());
    }

    public double getDouble() {
        return Double.parseDouble(nextToken());
    }

    public long getLong() {
        return Long.parseLong(nextToken());
    }

    public String getWord() {
        return nextToken();
    }

	public String getLine(){
        try{
            st = null;
            return r.readLine();
        }
        catch(IOException ex){}
        return null;
    }
	

    private BufferedReader r;
    private String line;
    private StringTokenizer st;
    private String token;

    private String peekToken() {
        if (token == null)
            try {
                while (st == null || !st.hasMoreTokens()) {
                    line = r.readLine();
                    if (line == null) return null;
                    st = new StringTokenizer(line);
                }
                token = st.nextToken();
            } catch (IOException e) { }
        return token;
    }

    private String nextToken() {
        String ans = peekToken();
        token = null;
        return ans;
    }
}
