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G - Cubic?

Score : $600$ points

Problem Statement

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 $x=y^3$.

Constraints

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

Input

Input is given from Standard Input in the following format:

$N$ $Q$

$A_1$ $A_2$ $\dots$ $A_N$

$L_1$ $R_1$

$L_2$ $R_2$

$\vdots$

$L_Q$ $R_Q$

Output

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.

8 5
7 49 30 1 15 8 6 10
1 2
2 3
4 4
5 8
3 8

Yes
No
Yes
No
Yes

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