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.*;

public class File {
    public 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 nextInt() {
            return Integer.parseInt(next());
        }

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

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }		
		
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
		
		
		
		int T = sc.nextInt();
		
		
		for (int t = 1; t <= T; t++) {
			long p = sc.nextLong();
			long q = sc.nextLong();
			
			
			long res = 1;
			
			if (p % q != 0) {
				res = p;
			}
			else {
				List<Long> factors = getFactors(q);
				
				long best = 1;
								
				for (long factor : factors) {
				    if (p % factor == 0) {
    					long X = p;
    					
    					while (X % q == 0) {
    						X /= factor;
    					}
    					
    					best = Math.max(best, X);
    				}
				}
				
				res = best;
			}
		    
			out.println(res);
		}
		
		
		
		
		
		out.close();
	}
	
	public static List<Long> getFactors(long num) {
		List<Long> res = new ArrayList();
		res.add(num);
		
		for (long d = 2; d <= (long)Math.sqrt(num); d++) {
			if (num % d == 0) {
				res.add(d);
				
				if ((num / d) != d) {
					res.add(num / d);
				}
			}
		}
		
		return res;
	}
}











	