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 Main {
	static final int M = 1000000007;
		static FastReader in = new FastReader();
		static PrintWriter out = new PrintWriter(System.out);
//		static Scanner in = new Scanner(System.in);
//        File file = new File("input.txt");
//        Scanner in = new Scanner(file);
//        PrintWriter out = new PrintWriter(new FileWriter("output.txt"));
    public static void main(String[] args) {    	
    	
    	int t = in.nextInt();
    	while(t-- > 0) {
    		long p = in.nextLong(), q = in.nextLong();
    		if(p%q!=0) {
    			out.println(p);
    		}else {
    			Map<Long,Long> qd = divisors(q);
                Long x = 0L;
                for(Map.Entry<Long,Long> e : qd.entrySet()){
                    Long pp = p;
                    Long qq = pow(e.getKey(), e.getValue());
                    while(pp%qq==0)
                        pp/=e.getKey();
                    x=Math.max(x, pp);
                }
                out.println(x);
    		}
    	}
    	
         
    	out.close(); 
    }

	private static Map<Long, Long> divisors(long n) {
		Map<Long, Long> d = new HashMap<>();
        for(Long i = 2L; i*i <= n; ++i){
            if(n%i==0){
                Long c =0L;
                while(n%i==0) {c++; n/=i;}
                d.put(i,c);
            }
        }
        if(n>=2L) d.put(n,1L);
        return d;
	}
	 private static Long pow(Long key, Long value) {
         if(value==0)
             return 1L;
         if(value==1)
             return key;
         if(value%2==1L)
             return key*pow(key,value-1);
         Long v = pow(key,value/2);
         return v*v;
     }

	static int gcd(int a, int b) {
    	if(b==0) return a;
    	return gcd(b, a%b);
    }
    
	static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            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());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}