For positive integers $X$ and $b\ge 2$, define $f(X,b)$ as a sequence which describes the base-$b$ representation of $X$, where the $i$-th element in the sequence is the $i$-th least significant digit in the base-$b$ representation of $X$. For example, $f(6,2)=\{0,1,1\}$, while $f(233,17)=\{12,13\}$.

Given four positive integers $x$, $y$, $A$ and $B$, please find two positive integers $a$ and $b$ satisfying:

• $2\le a\le A$
• $2\le b\le B$
• $f(x,a)=f(y,b)$

Input

There are multiple test cases. The first line of the input contains an integer $T$ ($1\le T\le 10^3$) indicating the number of test cases. For each test case:

The first line contains four integers $x$, $y$, $A$ and $B$ ($1\le x,y\le 10^9$, $2\le A,B\le 10^9$).

It's guaranteed that there are at most $50$ test cases satisfying $\max(x,y)>10^6$.

Output

For each test case, if valid positive integers $a$ and $b$ do not exist, output NO in one line.

Otherwise, first output YES in one line. Then in the next line, output two integers $a$ and $b$ separated by a space. If there are multiple valid answers, you can output any of them.

Examples

Input 1

6
1 1 1000 1000
1 2 1000 1000
3 11 1000 1000
157 291 5 6
157 291 3 6
10126 114514 789 12345

Output 1

YES
2 2
NO
YES
2 10
YES
4 5
NO
YES
779 9478