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  C{
	
	static class FastReader {
 
        BufferedReader br;
        StringTokenizer st;
 
        private 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());
        }
 
	 int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
	}
 
	int[] nextIntArrayOne(int n) {
				int[] a = new int[n+1];
				for (int i = 1; i < n+1; i++)
					a[i] = nextInt();
				return a;
	}
 
        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;
        }
    }
 
    public static void main(String[] args) {
    	FastReader s = new FastReader();
    	StringBuilder str = new StringBuilder();
 
		int t = s.nextInt();
		

		while(t-- >0) {
			long p = s.nextLong(); int q = s.nextInt();
			
			if(p % q != 0) {
				str.append(p+"\n");
				continue;
			}
			
			
			long ans = 1l;
			
			
			HashMap<Integer, Integer> factors = factors(q);
			
			long temp = p;
			for(Map.Entry<Integer, Integer> factorEntry : factors.entrySet()) {
				int factor = factorEntry.getKey();
				int count = factorEntry.getValue();
				
				int countInP = 0;
				
				while(temp  % factor == 0) {
					countInP++;
					temp /= factor;
				}
				
				int remove = Math.max(countInP - count + 1, 0);
				
				long cur = 1;
				
				while(remove-- > 0) cur *= factor;
				
				ans = Math.max(ans, p / cur);
				
				
				
			}
			
			
			
			
			str.append(ans+"\n");
			
			
		}
		System.out.println(str);
     }
    
    
 
    public static HashMap<Integer, Integer> factors(int n ){
 	   
  	  HashMap<Integer, Integer> map = new HashMap<>();
  	  int temp = n;
  	  
  	  while(n % 2 == 0) {
  		  
  		  if(map.containsKey(2)) {
  			  map.put(2, map.get(2) + 1);
  		  }else {
  			  map.put(2, 1);
  		  }
  		  
  		  n /= 2;
  	  }
  	  
  	  
  	  for(int i = 3; i * i <= temp; i+= 2) {
  		
  		  while(n % i == 0) {
  			if(map.containsKey(i)) {
    			  map.put(i, map.get(i) + 1);
    		  }else {
    			  map.put(i, 1);
    		  }
  			  n /= i;
  		  }
  			
  	  }
  	  
  	  if(n > 1) {
  		if(map.containsKey(n)) {
			  map.put(n, map.get(n) + 1);
		  }else {
			  map.put(n, 1);
		  }
  	  }
  	   
  	   return map;
  	}
   
 
 
	
 
}