Given a sequence $A$ of $N$ numbers, answer the following $Q$ questions.

-   In the $i$-th question, you are given integers $L_i$ and $R_i$. Is $A_{L_i} \times A_{L_i+1} \times \dots \times A_{R_i}$ a cubic number?

Here, a positive integer $x$ is said to be a cubic number when there is a positive integer $y$ such that $x=y^3$.

Input is given from Standard Input in the following format:

```
$N$ $Q$
$A_1$ $A_2$ $\dots$ $A_N$
$L_1$ $R_1$
$L_2$ $R_2$
$\vdots$
$L_Q$ $R_Q$
```

Print $Q$ lines.  
The $i$-th line should contain `Yes` if, in the $i$-th question, $A_{L_i} \times A_{L_i+1} \times \dots \times A_{R_i}$ is a cubic number, and `No` otherwise.  
The checker is case-insensitive; output can be either uppercase or lowercase.

-   All values in input are integers.
-   $1 \le N,Q \le 2 \times 10^5$
-   $1 \le A_i \le 10^6$
-   $1 \le L_i \le R_i \le N$

Yes
No
Yes
No
Yes

• For the first question, 7×49=343 is a cubic number.
• For the second question, 49×30=1470 is not a cubic number.
• For the third question, 1 is a cubic number.
• For the fourth question, 15×8×6×10=7200 is not a cubic number.
• For the fifth question, 30×1×15×8×6×10=216000 is a cubic number.