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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Division {
	static long get(long pi, long qi, long val) {
		if(val == 1)
			return 1;
		while(pi % qi == 0)
			pi /= val;
		return pi;
	}
	public static void main(String[] args)  {
		FastScanner fs = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		int testCase = fs.nextInt();
		for (int tc = 0; tc < testCase; tc++) {
			long pi = fs.nextLong();
			long qi = fs.nextLong();
			if(pi % qi != 0) {
				System.out.println(pi);
				continue;
			}
			long ans = 1;
			for(long i = 1; i <= (long)Math.sqrt(qi); ++i) {
				if(qi % i != 0)
					continue;
				ans = Math.max(ans, get(pi, qi, i));
				ans = Math.max(ans, get(pi, qi, qi / i));
			}
			System.out.println(ans);
		}
	}
	static void ruffleSort(int[] a) {
		int n = a.length;
		Random r = new Random();
		for(int i = 0; i < a.length; ++i) {
			int oi = r.nextInt(n), t = a[i];
			a[i] = a[oi];
			a[oi] = t;
		}
		Arrays.sort(a);
	}
	static void sort(int[] a)   {
		ArrayList<Integer> l = new ArrayList<>();
		for(int i : a) l.add(i);
		Collections.sort(l);
		for(int i = 0; i < a.length; ++i) a[i] = l.get(i);
	}
	static class FastScanner {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");

		String next()   {
			while(!st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a = new int[n];
			for(int i = 0; i < n; ++i)
				a[i] = nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
}