<image>

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.
import java.util.*;
import java.util.function.Function;
import java.util.function.ToDoubleFunction;
import java.util.function.ToIntFunction;
import java.util.function.ToLongFunction;
import java.io.*;
public class Main {
 
	static ArrayList<Integer> adj[];
	static char color[];
	static boolean b[],visited[],possible;
	static Map<Integer,HashSet<Integer>> s;
	static int totalnodes,colored;
	static int count[];
	static long sum[];
	public static void main(String[] args) throws IOException {
		
		
		in=new InputReader(System.in);
		w=new PrintWriter(System.out);
       int t=in.nextInt();
       while(t-->0)
       {
    	  long a=in.nextLong(),b=in.nextLong();
    	  long m=a*b;
    	  long ans=isCube(m);
    	 
          if(ans==-1)
        	  w.println("No");
          else
          {
        	  if(a%ans==0 && b%ans==0)
        		  w.println("Yes");
        	  else
        		  w.println("No");
          }
       }
	      
       w.close();			
		}
	public static long isCube(long n)
	{
		long x=0,y=1000001;
		while(x<=y)
		{
			long mid=(x+y)/2;
			if(mid*mid*mid==n)
				return (int)mid;
			else if(mid*mid*mid<n)
				x=mid+1;
			else
				y=mid-1;
		}
		return -1;
		
	}

	   public static int kadane (int a[])
	    {
	        int n = a.length;
	        int max_so_far = Integer.MIN_VALUE, max_ending_here = 0;
	        for (int i = 0; i < n; i++)
	        {
	            max_ending_here = max_ending_here + a[i];
	           
	            if (max_so_far < max_ending_here)
	                max_so_far = max_ending_here;
	            if (max_ending_here < 0)
	                max_ending_here = 0;
	        }
	        return max_so_far;
	    }
	public static int find_pivot(int[] a,int k)
	{
		int pivot=pivot_element(a,0,a.length-1);
		if(a[pivot]==k)
			 return pivot;
		else if(pivot==-1)
			 return binary_search(a,0,a.length-1,k);
		else if(a[0]<=k)
			 return binary_search(a,0,pivot-1,k);
		else 
			return binary_search(a,pivot+1,a.length-1,k);
		
	}
	public static int pivot_element(int[] a,int l,int r)
	{
	   if(r<l)
		   return -1;
	   if(r==l)
		   return l;
			int mid=(l+r)/2;
			 if (mid < r && a[mid] > a[mid + 1])
			       return mid;
			   if (mid > l && a[mid] < a[mid - 1])
			       return (mid-1);
			   if (a[l] >a[mid])
			       return pivot_element(a, l, mid-1);
			   return pivot_element(a, mid + 1, r);
		
	}
	public static int binary_search(int[] a,int l,int r,int k)
	{
		if(r<l)
			return -1;
		int mid=(l+r)/2;
		if(a[mid]==k)
			 return mid;
		else if(a[mid]>k)
			 return binary_search(a,l,mid-1,k);
		else
			 return binary_search(a,mid+1,r,k); 
	}
	public static String[] subString(String s, int n) 
	{
	    String[] st =new String[(n*n+n)/2];
	    for(int i=0;i<st.length;i++)
	    	st[i]="";
	    int l=0;
	    for (int len = 1; len <= n; len++) 
	    {    
	        // Pick ending point
	        for (int i = 0; i <= n - len; i++) 
	        {
	            //  Print characters from current
	            // starting point to current ending
	            // point.  
	            int j = i + len - 1;            
	            for (int k = i; k <= j; k++) 
	                st[l]+=s.charAt(k);
	      //w.println(st[l]);
	            l++;
	            //cout << endl;
	        }
	    }
	    return st;
	}
	  public static long factorial(long n)
	    {
	        long res = 1, i;
	        for (i=2; i<=n; i++)
	            res *= i;
	        return res;
	    }
	
   
	public static int factors(int n,int start){
		int count = 0;
		int i;
		for(i=1;i*i<n;i++)
			if(n%i == 0){
				if(i>start)	count++;
				if(n/i > start)	count++;
			}
		if(i*i == n && i>start)	count++;
		return count;
	}


 	public static int isPrime(int n){
	    int i;

	    if (n==2)
	        return 1;

	    if (n%2==0)
	        return 0;

	    for (i=3;i<=Math.sqrt(n);i+=2)
	        if (n%i==0)
	            return 0;

	    return 1;
	}

	
	static InputReader in;
	static PrintWriter w;
	public static void seive(long n){
		b = new boolean[(int) (n+1)];
	Arrays.fill(b, true);
		for(int i = 2;i*i<=n;i++){
			if(b[i]){
				sum[i]=count[i];
			//	System.out.println(sum[i]+" wf");
				for(int p = 2*i;p<=n;p+=i){
					b[p] = false;
					sum[i]+=count[p];  
					//System.out.println(sum[i]);
				}
			}
		
		}
	}
	static class Pair implements Comparable<Pair> {
		char c;
		int count;
		public Pair(){
			
		}
		public Pair(char u, int v) {
			this.c = u;
			this.count= v;
			
		}
		public int compareTo(Pair other) {
			
				return 0;
		}
		
		/*public String toString() {
			return "[u=" + u + ", v=" + v + "]";
		}*/
	}
	static class Node2{
		Node2 left = null;
		Node2 right = null;
		Node2 parent = null;
		int data;
	}
	
	//binaryStree
	static class BinarySearchTree{
		Node2 root = null;
		int height = 0;
		int max = 0;
		int cnt = 1;
		ArrayList<Integer> parent = new ArrayList<Integer>();
		HashMap<Integer, Integer> hm = new HashMap<Integer, Integer>();
		public void insert(int x){
			Node2 n = new Node2();
			n.data = x;
			if(root==null){
				root = n;
			}
			else{
				Node2 temp = root,temp2 = null;
				while(temp!=null){
					temp2 = temp;
					if(x>temp.data) temp = temp.right;
					else temp = temp.left;
				}
				if(x>temp2.data) temp2.right = n;
				else temp2.left = n;
				n.parent = temp2;
				parent.add(temp2.data);
			}
		}
		public Node2 getSomething(int x, int y, Node2 n){
			if(n.data==x || n.data==y) return n;
			else if(n.data>x && n.data<y) return n;
			else if(n.data<x && n.data<y) return getSomething(x,y,n.right);
			else return getSomething(x,y,n.left);
		}
		public Node2 search(int x,Node2 n){
			if(x==n.data){
				max = Math.max(max, n.data);
				return n;
			}
			if(x>n.data){
				max = Math.max(max, n.data);
				return search(x,n.right);
			}
			else{
				max = Math.max(max, n.data);
				return search(x,n.left);
			}
		}
		public int getHeight(Node2 n){
			if(n==null) return 0;
			height = 1+ Math.max(getHeight(n.left), getHeight(n.right));
			return height;
		}
	}
public static void debug(Object... o) {
	System.out.println(Arrays.deepToString(o));
}
 
public static String rev(String s)
{
	StringBuilder sb=new StringBuilder(s);
	sb.reverse();
	return sb.toString();
}
 
static long lcm(long a, long b)
{
    return a * (b / gcd(a, b));
}
 
static long gcd(long a, long b)
{
    while (b > 0)
    {
        long temp = b;
        b = a % b; // % is remainder
        a = temp;
    }
    return a;
}
 
public static long max(long x, long y, long z){
		if(x>=y && x>=z) return x;
		if(y>=x && y>=z) return y;
		return z;
	}
	static int[] sieve(int n,int[] arr)
	{
	for(int i=2;i*i<=n;i++)
	{
		if(arr[i]==0)
		{
			for(int j=i*2;j<=n;j+=i)
				arr[j]=1;
		}
	}
	return arr;
	}
 
 
 
 
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) {
	 return nextIntArray(n, 0);
	    }
	    
public int[] nextIntArray(int n, int off) {
	 int[] arr = new int[n + off];
	   for (int i = 0; i < n; i++) {
	    arr[i + off] = nextInt();
	    }
	    return arr;
	    }
	    
public long[] nextLongArray(int n) {
return nextLongArray(n, 0);
	    }
        
	public long[] nextLongArray(int n, int off) {
	 long[] arr = new long[n + off];
	 for (int i = 0; i < n; i++) {
		  arr[i + off] = nextLong();
		 }
 return arr;
	}
 
 
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);
}
}
	
}