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.math.BigInteger;
import java.util.*;
public class Main {
    final static long mod = 1000000007;
    static void debug(Object...args){System.out.println(Arrays.deepToString(args));}
    public static void main(String[] args) throws Exception {
        InputReader sc = new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        Random gen = new Random();
        int test = sc.nextInt();
        while (test-- > 0) {
            //StringBuffer sb = new StringBuffer();
            long p = sc.nextLong();
            long q = sc.nextLong();
            long pp = p;
            if(p%q!=0)
            {
                pw.println(p);
                continue;
            }

            long q2 = q;
            ArrayList<Long> l = new ArrayList<>();
            for(int i=2;i*i<=q2;i++)
            {
                if(q2%i==0)
                {
                    l.add((long) i);
                    while(q2%i==0)
                        q2/=i;
                }

            }
            if(q2>1)
                l.add(q2);

            long ans = p;
            for(long i  : l)
            {
                long pcpy = p;
                long qcpy = q;

                int a = 0;
                int b = 0;

                while(pcpy%i==0)
                {
                    pcpy/=i;
                    ++a;
                }

                while(qcpy % i==0)
                {
                    qcpy/=i;
                    ++b;
                }

                long temp = 1;

                while(a >= b)
                {
                    temp*=i;
                    --a;
                }

                ans = Math.min(ans,temp);
            }
            pw.println(p/ans);

        }

        pw.flush();
        pw.close();

    }


    static class Data implements Comparable<Data>{
        int x;
        int y;

        public Data (int m, int n) {
            x = m;
            y = n;

        }
        @Override
        public int compareTo(Data o) {

            return x-o.x;
        }
    }

    static class InputReader {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;

        public InputReader(InputStream st) {
            this.stream = st;
        }

        public int read() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int [] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }
        public long[] nextLongArray(int n) {
            long [] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextLong();
            }
            return a;
        }

        public static int[] shuffle(int[] a, Random gen)
        { for(int i = 0, n = a.length;i < n;i++)
        { int ind = gen.nextInt(n-i)+i;
            int d = a[i];
            a[i] = a[ind];
            a[ind] = d;

        }
            return a;
        }
        public static long[] shuffle(long[] a, Random gen)
        { for(int i = 0, n = a.length;i < n;i++)
        { int ind = gen.nextInt(n-i)+i;
            long d = a[i];
            a[i] = a[ind];
            a[ind] = d;

        }
            return a;
        }


        public String readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

    }

}
