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.*;

public class Main{
	
	static int mod=(int)1e9+7;
	
	public static void main(String[] args) throws IOException {
		Writer out=new Writer(System.out);
		Reader in=new Reader(System.in);
		int ts=in.nextInt();
		outer: while(ts-->0) {	
			
			long p=in.nextLong();
			long q=in.nextLong();
			
			if(p<q || p%q!=0) {
				out.println(p);
				continue outer;
			}
			
			long temp=p;
			long min=Long.MAX_VALUE;
			int root=1;
			for(root=2; root*root<=q; root++);
			root--;
			for(long i=2; i*i<=q; i++) {
				
				long cnt1=countFactors(temp,i);
				long cnt2=countFactors(q,i);
				if(cnt2!=0)	min=min(min,pow(i,cnt1-cnt2+1));
				
				if(q%i==0 && q/i>root) {
					cnt1=countFactors(temp,q/i);
					cnt2=countFactors(q,q/i);
					if(cnt2!=0)	min=min(min,pow(q/i,cnt1-cnt2+1));
				}
				
				
			}
			
			long cnt1=countFactors(temp,q);
			min=min(min,pow(q,cnt1));
			
			out.println(p/min);
			
			
			
			
		}
		
		out.close();		
		
	}
	

	static int countFactors(long n, long m) {
	
		int count=0;
		while(n%m==0) {
			n/=m; count++;
		}
		return count;
		
	}
	
	
/*********************************** UTILITY CODE BELOW **************************************/	
	static int abs(int a) {
		return a>0 ? a : -a;
	}
	
	static int max(int a, int b) {
		return a>b ? a : b;
	}
	
	static long min(long a, long b) {
		return a<b ? a : b;
	}
	
	static int min(int a, int b) {
		return a<b ? a : b;
	}
	
	static int pow(int n, int m) {
		if(m==0) return 1;
		long temp=pow(n,m/2);
		long res=((temp*temp)%mod);
		if(m%2==0) return (int)res;
		return (int)((res*n)%mod);
	}
	
	static long pow(long n, long m) {
		
		if(m==0) return 1;
		long temp=pow(n,m/2);
		long res=temp*temp;
		if(m%2==0) return res;
		return res*n;
		
	}
	
	
	
	static class Pair{
		int u, v;
		
		Pair(int u, int v){this.u=u; this.v=v;}
		
		static void sort(Pair [] coll) {		
			List<Pair> al=new ArrayList<>(Arrays.asList(coll));
			Collections.sort(al,new Comparator<Pair>() {
				public int compare(Pair p1, Pair p2) {
					return p1.u-p2.u;
				}	
			});
			for(int i=0; i<al.size(); i++) {
				coll[i]=al.get(i);
			}
		}
		
	}
	
	static void sort(int[] a) {
		ArrayList<Integer> list=new ArrayList<>();
		for (int i:a) list.add(i);
		Collections.sort(list);
		for (int i=0; i<a.length; i++) a[i]=list.get(i);
	}
	
	static void sort(long a[]) {
		ArrayList<Long> list=new ArrayList<>();
		for(long i: a) list.add(i);
		Collections.sort(list);
		for(int i=0; i<a.length; i++) a[i]=list.get(i);
	}
	
	static int [] array(int n, int value) {	
		int a[]=new int[n];
		for(int i=0; i<n; i++) a[i]=value;
		return a;
	}
	
	static class Reader{
		
		BufferedReader br;
		StringTokenizer to;
		
		Reader(InputStream stream){
			br=new BufferedReader(new InputStreamReader(stream));
			to=new StringTokenizer("");
		}
		
		String next() {
			while(!to.hasMoreTokens()) {
				try {
					to=new StringTokenizer(br.readLine());	
				}catch(IOException e) {}
				
			}
			return to.nextToken();
			
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		
		long nextLong() {
			return Long.parseLong(next());
		}
		
		int [] readArray(int n) {
			int a[]=new int[n];
			for(int i=0; i<n ;i++) a[i]=nextInt();
			return a;
		}
		long [] readLongArray(int n) {
			long a[]=new long[n];
			for(int i=0; i<n ;i++) a[i]=nextLong();
			return a;
		}
		
	}
	
	static class Writer extends PrintWriter{
		Writer(OutputStream stream){
			super(stream);
		}
		void println(int [] array) {
			for(int i=0; i<array.length; i++) {
				print(array[i]+" ");
			}
			println();
		}
		void println(long [] array) {
			for(int i=0; i<array.length; i++) {
				print(array[i]+" ");
			}
			println();
		}
	}
	
}