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Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.

The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.

Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.

Input

In the first string, the number of games n (1 ≤ n ≤ 350000) is given.

Each game is represented by a pair of scores a, b (1 ≤ a, b ≤ 109) – the results of Slastyona and Pushok, correspondingly.

Output

For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.

You can output each letter in arbitrary case (upper or lower).

Example

Input

6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000


Output

Yes
Yes
Yes
No
No
Yes

Note

First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.

The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
//package codeforces426;


import java.util.*;
import java.io.*;
import java.math.BigInteger;

/**
 *
 * @author rohan
 */

public class ProblemC {

    static long mod = (int) (1e9+7);
    
    
    static int prev=0;
   
    static void solve() {
	
        int t = sc.nextInt();
        while(t-->0)
        {
            long a = sc.nextLong();
            long b = sc.nextLong();
            
            long x = a*b;
            long y = (long)Math.cbrt(x);
            if((y*y*y)==x)
            {
                if(a%y==0&&b%y==0)
                    out.println("Yes");
                else
                    out.println("No");
            }
                
            else
                out.println("No");
            
        }
        out.close();

    }
    
    
    
    
    
    static InputReader sc = new InputReader(System.in);
    static PrintWriter out = new PrintWriter(System.out); 
    public static void main(String[] args) {

        new Thread(null,new Runnable() {
            @Override
            public void run() {
                try{
                    solve();
                }
                catch(Exception e){
                    e.printStackTrace();
                }
            }
        },"1",1<<26).start();
    }

    static class Pair implements Comparable<Pair>{

        int x,y,i;
        
	Pair (int x,int y,int i){
		this.x = x;
		this.y = y;
                this.i = i;
	}
        
        Pair (int x,int y){
		this.x = x;
		this.y = y;
	}
        
	public int compareTo(Pair o) {
                    return -Integer.compare(this.i,o.i);
		//return 0;
	}

        public boolean equals(Object o) {
            if (o instanceof Pair) {
                Pair p = (Pair)o;
                return p.x == x && p.y==y;
            }
            return false;
        }

        @Override
        public String toString() {
            return x + " "+ y + " "+i;
        }
        
        public int hashCode() {
            return new Long(x).hashCode() * 31 + new Long(y).hashCode();
        }
    
    } 


    static class Merge {

        public static void sort(int inputArr[]) {
            int length = inputArr.length;
            doMergeSort(inputArr,0, length - 1);
        }

        private static void doMergeSort(int[] arr,int lowerIndex, int higherIndex) {        
            if (lowerIndex < higherIndex) {
                int middle = lowerIndex + (higherIndex - lowerIndex) / 2;
                doMergeSort(arr,lowerIndex, middle);
                doMergeSort(arr,middle + 1, higherIndex);
                mergeParts(arr,lowerIndex, middle, higherIndex);
            }
        }

        private static void mergeParts(int[]array,int lowerIndex, int middle, int higherIndex) {
            int[] temp=new int[higherIndex-lowerIndex+1];
            for (int i = lowerIndex; i <= higherIndex; i++) {
                temp[i-lowerIndex] = array[i];
            }
            int i = lowerIndex;
            int j = middle + 1;
            int k = lowerIndex;
            while (i <= middle && j <= higherIndex) {
                if (temp[i-lowerIndex] < temp[j-lowerIndex]) {
                    array[k] = temp[i-lowerIndex];
                    i++;
                } else {
                    array[k] = temp[j-lowerIndex];
                    j++;
                }
                k++;
            }
            while (i <= middle) {
                array[k] = temp[i-lowerIndex];
                k++;
                i++;
            }
            while(j<=higherIndex){
                array[k]=temp[j-lowerIndex];
                k++;
                j++;
            }
        }

    }

    static long add(long a,long b){
        long x=(a+b);
        while(x>=mod) x-=mod;
        return x;
    }

    static long sub(long a,long b){
        long x=(a-b);
        while(x<0) x+=mod;
        return x;
    }

    static long mul(long a,long b){
        a%=mod;
        b%=mod;
        long x=(a*b);
        return x%mod;
    }


    static boolean isPal(String s){
        for(int i=0, j=s.length()-1;i<=j;i++,j--){
                if(s.charAt(i)!=s.charAt(j)) return false;
        }
        return true;
    }
    static String rev(String s){
                StringBuilder sb=new StringBuilder(s);
                sb.reverse();
                return sb.toString();
    }

    static long gcd(long x,long y){
        if(y==0)
                return x;
        else
                return gcd(y,x%y);
    }

    static int gcd(int x,int y){
        if(y==0)
                return x;
        else 
                return gcd(y,x%y);
    }

    static long gcdExtended(long a,long b,long[] x){

        if(a==0){
            x[0]=0;
            x[1]=1;
            return b;
        }
        long[] y=new long[2];
        long gcd=gcdExtended(b%a, a, y);

        x[0]=y[1]-(b/a)*y[0];
        x[1]=y[0];

        return gcd;
    }


    static long mulmod(long  a,long b,long m) {
        if (m <= 1000000009) return a * b % m;

        long res = 0;
        while (a > 0) {
            if ((a&1)!=0) {
                res += b;
                if (res >= m) res -= m;
            }
            a >>= 1;
            b <<= 1;
            if (b >= m) b -= m;
        }
        return res;
    }

    static int abs(int a,int b){
        return (int)Math.abs(a-b);
    }

    public static long abs(long a,long b){
        return (long)Math.abs(a-b);
    }

    static int max(int a,int b){
        if(a>b)
                return a;
        else
                return b;
    }

    static int min(int a,int b){
        if(a>b)
                return b;
        else 
                return a;
    }

    static long max(long a,long b){
        if(a>b)
                return a;
        else
                return b;
    }

    static long min(long a,long b){
        if(a>b)
                return b;
        else 
                return a;
    }

    static long pow(long n,long p,long m){
         long  result = 1;
          if(p==0)
            return 1;

        while(p!=0)
        {
            if(p%2==1)
                result *= n;
            if(result>=m)
            result%=m;
            p >>=1;
            n*=n;
            if(n>=m)
            n%=m;
        }
        return result;
    }

    static long pow(long n,long p){
        long  result = 1;
          if(p==0)
            return 1;

        while(p!=0)
        {
            if(p%2==1)
                result *= n;	    
            p >>=1;
            n*=n;	    
        }
        return result;
    }

    static void debug(Object... o) {
            System.out.println(Arrays.deepToString(o));
    }

    static class InputReader {

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

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

        public int snext() {
                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 = snext();
                while (isSpaceChar(c)) {
                        c = snext();
                }
                int sgn = 1;
                if (c == '-') {
                        sgn = -1;
                        c = snext();
                }
                int res = 0;
                do {
                        if (c < '0' || c > '9')
                                throw new InputMismatchException();
                        res *= 10;
                        res += c - '0';
                        c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
        }

        public long nextLong() {
                int c = snext();
                while (isSpaceChar(c)) {
                        c = snext();
                }
                int sgn = 1;
                if (c == '-') {
                        sgn = -1;
                        c = snext();
                }
                long res = 0;
                do {
                        if (c < '0' || c > '9')
                                throw new InputMismatchException();
                        res *= 10;
                        res += c - '0';
                        c = snext();
                } 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 String readString() {
                int c = snext();
                while (isSpaceChar(c)) {
                        c = snext();
                }
                StringBuilder res = new StringBuilder();
                do {
                        res.appendCodePoint(c);
                        c = snext();
                } while (!isSpaceChar(c));
                return res.toString();
        }

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

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

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

        public interface SpaceCharFilter {
                public boolean isSpaceChar(int ch);
        }

    }
} 