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

public class A {
	static FastReader f = new FastReader();
	static PrintWriter out = new PrintWriter(System.out);

	public static void main(String[] args) {
		pre();
		int t = f.nextInt();

		while(t-- > 0) {
			solve();
		}
		out.close();
	}

	static ArrayList<Integer> primes = new ArrayList<>();
	static void pre() {
		boolean arr[] = new boolean[31624];

		for(int i=2;i<arr.length;i++) {
			if(!arr[i]) {
				for(int j=i*i;j<arr.length;j+=i) {
					arr[j] = true;
				}
			}
		}

		for(int i=2;i<arr.length;i++) {
			if(!arr[i]) {
				primes.add(i);
			}
		}
	}

	static void solve() {
		long p = f.nextLong();
		long q = f.nextLong();
		long ans = 1;

		for(int i : primes) {
			//System.out.println(i);
			int cnt = 0;
			while(q % i == 0) {
				q /= i;
				cnt++;
			}
			//System.out.println("asd"+cnt);
			long loc = p;
			int cnt2 = 0;
			
			while(loc % i == 0) {
				cnt2++;
				loc /= i;
			}
			//System.out.println("asd2"+cnt2);
			long num = 1;
			while(cnt <= cnt2 && cnt2 > 0) {
				cnt2--;
				num *= i;
			}
			if(cnt > cnt2) {
				//System.out.println(p+" "+num);
				ans = Math.max(ans, p/num);
			}
			
		}

		if(q > 1) {
			int cnt = 1;

			long loc = p;
			int cnt2 = 0;
			
			while(loc % q == 0) {
				cnt2++;
				loc /= q;
			}

			long num = 1;
			while(cnt <= cnt2 && cnt2 > 0) {
				cnt2--;
				num *= q;
			}
			if(cnt > cnt2) {
				//System.out.println(p+" "+num);
				ans = Math.max(ans, p/num);
			}
		}

		System.out.println(ans);
	}
	

	static class FastReader {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st;

		String next() {
			while(st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch(IOException ioe) {
					ioe.printStackTrace();
				}
			}
			return st.nextToken();
		}

		String nextLine() {
			String s = "";
			try {
				s = br.readLine();
			} catch(IOException ioe) {
				ioe.printStackTrace();
			}

			return s;
		}

		int  nextInt() {
			return Integer.parseInt(next());
		}

		double  nextDouble() {
			return Double.parseDouble(next());
		}

		long  nextLong() {
			return Long.parseLong(next());
		}
	}
}

