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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Collections;
import java.util.HashMap;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class B implements Runnable {

	public static void main(String[] args) throws Exception {

		new Thread(null, new B(), "SwapnilGanguly", 1 << 26).start();
	}

	static long Pow(long x, long y) {

		if (y == 0)
			return 1L;

		long p = Pow(x, y / 2);
		p = (p * p);

		if (y % 2 == 0)
			return p;

		else
			return (x * p);
	}

	public void run() {

		MyScanner sc = new MyScanner();
		PrintWriter pr = new PrintWriter(System.out);

		/*
		 * String s = sc.nextLine(); String[] st = s.split(" ");
		 * 
		 * int len = s.length() - (st.length - 1); int ceil =
		 * (int)Math.ceil(Math.sqrt(len)); int floor = (int)Math.floor(Math.sqrt(len));
		 */

		int T = sc.nextInt();

		while (T-- > 0) {

			long p = sc.nextLong(), q = sc.nextLong();

			if (q > p || p % q != 0) {

				pr.println(p);
				continue;
			}

			HashMap<Long, Long> map = new HashMap<>();
			TreeMap<Long, Long> weight = new TreeMap<>();
			
			for (long i = 2; i * i <= q; i++) {

				if (q % i == 0) {

					long pow = 1L, count = 0L;
					while (q % i == 0) {

						pow *= i;
						q /= i;
						count++;
					}
					
					//System.out.println(i + " " + count);
					map.put(i, count);
					weight.put(pow, i);
				}
			}
			
			if (q > 1) {
				
				map.put(q, 1L);
				weight.put(q, q);
			}

			/*for (long x : map.keySet())
				System.out.println(x + " " + map.get(x));*/
			
			/*for (long factor : map.keySet()) {

				long pow = Pow(factor, map.get(factor));
				if (p % pow == 0) {

					ans = p / pow;
					//System.out.println(pow);
					break;
				}
			}*/
			
			long ans = 0, x = p;
			for(long w : weight.keySet()) {
				
				//System.out.println(w);
				if(p % w == 0) {
					
					long factor = weight.get(w), count = map.get(factor);
					while(p % factor == 0)
						p /= factor;
					
					ans = Math.max(ans, p * Pow(factor, count - 1));
				}
				p = x;
			}
			pr.println(ans);
		}

		pr.close();
	}

	public static class MyScanner {
		BufferedReader br;
		StringTokenizer st;

		public MyScanner() {
			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;
		}
	}
}
