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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.
import java.io.*;
import java.math.*;
import java.security.KeyStore.Entry;
import java.util.*;
/* 
																yash jobanputra
																	DA-IICT
*/
public class yash {
	private static InputStream stream;
	private static byte[] buf = new byte[1024];
	private static int curChar;
	private static int numChars;
	private static SpaceCharFilter filter;
	private static PrintWriter pw;
	private static long mod = 1000000000 + 7;
	private static long mod1 = 1000000000 + 9;
	private static int MAX=1000001;
	private static int block;
	private static int[] cost;
	private static int times;
	private static boolean[] vis;
	private static void soln(){
		int n=ni();
		for(int i=0;i<n;i++)
		{
			long a=nl();long b=nl();
			long g=gcd(a,b);
			long p=a*b;
			long pq=(int)Math.cbrt(p);
			if((pq*pq*pq)!=p)
				pw.println("No");
			else if(g%pq==0)
				pw.println("yes");
			else
				pw.println("No");
		}
	}	
	public static long f(int number) {
	      if (number <= 1) return 1;
	      else return number * f(number - 1);
	   }
	public static void dfs(ArrayList<Integer>[] gr,int v)
	{
		vis[v]=true;
		ArrayList<Integer> arr=gr[v];
		for(int i=0;i<arr.size();i++)
		{
			if(!vis[arr.get(i)])
			{
				times++;
				dfs(gr,arr.get(i));
			}	
		}
		
	}
	private static class Pair implements Comparable<Pair>{
		int v,i,k;Pair j;
		public Pair(int a,int b){
			v=a;
			i=b;
		}
		@Override
		public int compareTo(Pair arg0) {
			{
				return this.v-arg0.v;
			}
		}
	}
	private static long pow(long a, long b, long c) {
		if (b == 0)
			return 1;
		long p = pow(a, b / 2, c);
		p = (p * p) % c;
		return (b % 2 == 0) ? p : (a * p) % c;
	}
	private static long gcd(long n, long l) {
		if (l == 0)
			return n;
		return gcd(l, n % l);
	}

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

	private static long min(long a, long b) {
		if (a < b)
			return a;
		return b;
	}

	public static void main(String[] args) throws Exception {
		new Thread(null,new Runnable(){
			@Override
			public void run() {
				/*try {
					InputReader(new FileInputStream("C:\\Users\\hardik\\Desktop\\C-small-1-attempt1.in"));
				} catch (FileNotFoundException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}*/
				InputReader(System.in);
				pw = new PrintWriter(System.out);
				/*try {
					pw=new PrintWriter(new FileOutputStream("C:\\Users\\hardik\\Desktop\\out.txt"));
				} catch (FileNotFoundException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}*/
				soln();
				pw.close();
			}
		},"1",1<<26).start();
	}

	public static void InputReader(InputStream stream1) {
		stream = stream1;
	}

	private static boolean isWhitespace(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

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

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

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

	private static long nl() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}
	private static double nd()
    {
        double ret = 0, div = 1;
        int c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();

        do {
            ret = ret * 10 + c - '0';
        }
        while ((c = read()) >= '0' && c <= '9');

        if (c == '.')
        {
            while ((c = read()) >= '0' && c <= '9')
            {
                ret += (c - '0') / (div *= 10);
            }
        }

        if (neg)
            return -ret;
        return ret;
    }
	private static String nextToken() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	private static String nli() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isEndOfLine(c));
		return res.toString();
	}
	
	private static int[] nia(int n) {
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = ni();
		}
		return arr;
	}

	private static long[] nla(int n) {
		long[] arr = new long[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nl();
		}
		return arr;
	}

	private static void pa(int[] arr) {
		for (int i = 0; i < arr.length; i++) {
			pw.print(arr[i] + " ");
		}
		pw.println();
		return;
	}

	private static void pa(long[] arr) {
		for (int i = 0; i < arr.length; i++) {
			pw.print(arr[i] + " ");
		}
		pw.println();
		return;
	}

	private static boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}
	private static char nc() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		char c1=(char)c;
		while(!isSpaceChar(c))
			c=read();
		return c1;
	}
	public String ns() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }
	private interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}