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 $x=y^3$. - All values in input are integers. - $1 \le N,Q \le 2 \times 10^5$ - $1 \le A_i \le 10^6$ - $1 \le L_i \le R_i \le N$

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

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.