Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.

To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that: 

  * p_i is divisible by x_i; 
  * x_i is not divisible by q_i. 

Oleg is really good at division and managed to find all the answers quickly, how about you?

Input

The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.

Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.

Output

Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.

One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.

Example

Input


3
10 4
12 6
179 822


Output


10
4
179

Note

For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.

For the second pair, where p_2 = 12 and q_2 = 6, note that 

  * 12 is not a valid x_2, since 12 is divisible by q_2 = 6; 
  * 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6. 

The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6.
import java.io.*;
import java.util.ArrayList;
import java.util.List;

public class Division {
    public static void main(String[] args) throws Exception {
        // BufferedReader br = new BufferedReader(new FileReader(new File("input.txt")));
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        handleMultipleTestCases(br);
    }

    private static void handleMultipleTestCases(BufferedReader br) throws Exception {
        int T = readInt(br);
        for (int tc = 0; tc < T; tc++) {
            handleTestCase(br);
        }
    }

    private static void handleTestCase(BufferedReader br) throws Exception {
        String[] line = br.readLine().split(" ");
	long p = Long.parseLong(line[0]);
	int q = Integer.parseInt(line[1]);
	System.out.println(getDivision(p,q));
    }

    private static int readInt(BufferedReader br) throws Exception {
        return Integer.parseInt(br.readLine());
    }

    private static int[] readArrInt(BufferedReader br) throws Exception {
        String[] line = br.readLine().split(" ");
        int[] arr = new int[line.length];
        for (int i = 0; i < line.length; i++) {
            arr[i] = Integer.parseInt(line[i]);
        }
        return arr;
    }

    private static List<Integer> readList(BufferedReader br) throws Exception {
        String[] line = br.readLine().split(" ");
        List<Integer> arr = new ArrayList<>();
        for (int i = 0; i < line.length; i++) {
            arr.add(Integer.parseInt(line[i]));
        }
        return arr;
    }

    private static void print(int[][] mat) {
        System.out.println("----------------------------------------");
        for (int i = 0; i < mat.length; i++) {
            System.out.print("{");
            for (int j = 0; j < mat[0].length; j++) {
                System.out.print(mat[i][j] + " ");
            }
            System.out.println("}");
        }
        System.out.println("----------------------------------------");
    }

    private static void print(int[] mat) {
        System.out.print("{");
        for (int i = 0; i < mat.length; i++) {
            System.out.print(mat[i] + " ");
        }
        System.out.println("}");
    }

    private static long getDivision(long p, int q){
	if(p%q!=0){
		return p;
	} else {
		long x =1;
		for(long i=1; i<=Math.sqrt(q); i++) {
			if(q%i==0) {
				long Xm = p;
				while(i!=1 && Xm%i==0) {
					Xm = Xm/i;
					if(Xm%q!=0) {
						x = Math.max(Xm,x);
						break;
					}
				}
				Xm = p;
				while(Xm%(q/i)==0){
					Xm= Xm/(q/i);
					if(Xm%q!=0) {
                                                x = Math.max(Xm,x);
                                                break;
                                        }
				}
			}
		}
		return x;
	}
    }
}

