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.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter pw = new PrintWriter(System.out);
    static int MOD = 1000000007;

    public static void main(String[] args) throws IOException {
        Main m = new Main();
        m.solve();
        m.close();
    }

    void close() throws IOException {
        pw.flush();
        pw.close();
        br.close();
    }

    int readInt() throws IOException {
        return Integer.parseInt(br.readLine());
    }

    long readLong() throws IOException {
        return Long.parseLong(br.readLine());
    }

    int[] readIntLine() throws IOException {
        String[] tokens = br.readLine().split(" ");
        int[] A = new int[tokens.length];
        for (int i = 0; i < A.length; i++)
            A[i] = Integer.parseInt(tokens[i]);
        return A;
    }

    long[] readLongLine() throws IOException {
        String[] tokens = br.readLine().split(" ");
        long[] A = new long[tokens.length];
        for (int i = 0; i < A.length; i++)
            A[i] = Long.parseLong(tokens[i]);
        return A;
    }

    void solve() throws IOException {
        int t = readInt();
        for (int ti = 0; ti < t; ti++) {
            long[] nk = readLongLine();
            long n = nk[0];
            long k = nk[1];
            long sum = (k - 1) * (k - 1);
            long left = n - sum;
            if (left < 0 || left % 2 == 0 || left < 2 * (k-1) + 1) {
                pw.println("NO");
            } else {
                pw.println("YES");
            }
        }
    }
}