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.*;
import java.math.*;
 
 
//Sub_To_Errichto
public class Main {
    static final long MOD = 1000000007L;
    static final long MOD2 = 1000000009L;
    //static final long MOD = 998244353L;
    static final int INF = 50000000;
    static final int NINF = -500000000;
    

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter pw = new PrintWriter(System.out);
        
        int Q = sc.ni();
        for (int q = 0; q < Q; q++) {
        	long A = sc.nl();
        	long B = sc.nl();
        	if (A%B!=0) {
        		pw.println(A);
        		continue;
        	}
        	HashMap<Long,Integer> div = new HashMap<Long,Integer>();
        	long N = B;
        	for (long i = 2; i*i <= B; i++) {
        		int cnt = 0;
        		while (N%i==0) {
        			cnt++;
        			N /= i;
        		}
        		if (cnt>0)div.put(i, cnt);
        	}
        	if (N > 1) div.put(N, 1);
        	long ans = 1;
        	for (long d: div.keySet()) {
        		int pow = div.get(d);
        		long res = A;
        		while (res % d == 0) {
        			res /= d;
        		}
        		for (int i = 0; i < pow-1; i++)
        			res *= d;
        		ans = Math.max(ans, res);
        	}
        	pw.println(ans);
        }
        pw.close();
    }
 
    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
 
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int ni() {
            return Integer.parseInt(next());
        }
 
        long nl() {
            return Long.parseLong(next());
        }
 
        double nd() {
            return Double.parseDouble(next());
        }
 
        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}