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_1445 {
	
	public static ArrayList<Long> factorsDiv(long n) {
		ArrayList<Long> factors = new ArrayList<>();
		ArrayList<Long> factors2 = new ArrayList<>();
		for(int i = 1; 1l * i * i <= n; i++)
			if(n % i == 0) {
				factors.add(1l * i);
				if(1l * i * i != n)
					factors2.add(1l * n / i);
			}
		for(int i = factors2.size() - 1; i >= 0; i--)
			factors.add(factors2.get(i));
		return factors;
	}
	
	static ArrayList<Integer> primes;
	static boolean[] isPrime;
	public static void sieve(int n) {
		primes = new ArrayList<Integer>();
		isPrime = new boolean[n + 1];
		Arrays.fill(isPrime, true);
		isPrime[0] = isPrime[1] = false;
		for(int i = 2; i <= n; i++) {
			if(isPrime[i]) {
				if(1l * i * i <= n)
					for(int j = i * i; j <= n; j += i)
						isPrime[j] = false;
				primes.add(i);
			}
		}
	}
	
	static ArrayList<Long> primeFactor;
	static ArrayList<Integer> primeFactorCount;
	public static void primeFactors(long n) {
		primeFactor = new ArrayList<>();
		primeFactorCount = new ArrayList<>();
		
		for(int p : primes) {
			if(n == 1)
				break;
			if(1l * p * p > n)
				break;
			
			int cnt = 0;
			while(n % p == 0) {
				n /= p;
				cnt++;
			}
			
			if(cnt > 0) {
				primeFactor.add(1l * p);
				primeFactorCount.add(cnt);
			}
		}
		
		if(n > 1) {
			primeFactor.add(n);
			primeFactorCount.add(1);
		}
	}
	
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		
		sieve((int)(Math.sqrt((int)1e9) + 5));
		int t = sc.nextInt();
		while(t-->0) {
			long p = sc.nextLong(), q = sc.nextLong();
			if(p < q) {
				pw.println(p);
			} else if(p == q){
				ArrayList<Long> facp = factorsDiv(p);
				pw.println(facp.get(facp.size() - 2));
			} else {
				if(p % q != 0) {
					pw.println(p);
				} else {
					primeFactors(q);
					long max = 0;
					for(int i = 0; i < primeFactor.size(); i++) {
						long ans = p;
						long fac = primeFactor.get(i);
						while(ans % fac == 0)
							ans /= fac;
						for(int j = 0; j < primeFactorCount.get(i) - 1; j++)
							ans *= fac;
						max = Math.max(max, ans);
					}
					pw.println(max);
				}
			}
		}
		
		pw.flush();
	}

	public static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

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

		public int[] nextIntArray(int n) throws IOException {
			int[] array = new int[n];
			for (int i = 0; i < n; i++)
				array[i] = nextInt();
			return array;
		}

		public Integer[] nextIntegerArray(int n) throws IOException {
			Integer[] array = new Integer[n];
			for (int i = 0; i < n; i++)
				array[i] = new Integer(nextInt());
			return array;
		}

		public long[] nextLongArray(int n) throws IOException {
			long[] array = new long[n];
			for (int i = 0; i < n; i++)
				array[i] = nextLong();
			return array;
		}

		public double[] nextDoubleArray(int n) throws IOException {
			double[] array = new double[n];
			for (int i = 0; i < n; i++)
				array[i] = nextDouble();
			return array;
		}

		public static int[] shuffle(int[] a) {
			int n = a.length;
			Random rand = new Random();
			for (int i = 0; i < n; i++) {
				int tmpIdx = rand.nextInt(n);
				int tmp = a[i];
				a[i] = a[tmpIdx];
				a[tmpIdx] = tmp;
			}
			return a;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}
