Problem Statement

The fairy has $N$ boxes, and the $i$-th box contains $A_i$ apples.
The fairy is about to hold a banquet with many fairy friends, and plans to open some of the boxes and distribute the apples.
The fairy has come up with $Q$ plans. In the $i$-th plan, $P_i$ fairies will come, and the fairy intends to open all the boxes in $[L_i, R_i]$ and share the apples inside.
At this time, by the power of magic, $\prod_{j=L_i}^{R_i} A_j$ apples can be taken out.
For each plan, output Yes if the apples taken out can be distributed equally among exactly $P_i$ fairies, and NO if there will inevitably be a remainder.

Input

$N$
$A_1$ $A_2$ $\cdots$ $A_N$
$Q$
$P_1$ $L_1$ $R_1$
$P_2$ $L_2$ $R_2$
$\vdots$
$P_Q$ $L_Q$ $R_Q$

Constraints
・$1 \leq N, Q \leq 10^5$
・$0 \leq A_i \leq 2 \times 10^3$
・$1 \leq L_i \leq R_i \leq N$
・$1 \leq P_i \leq 10^9$
・All inputs are integers

Output

On the $i$-th line, output Yes if $\prod_{j=L_i}^{R_i} A_j$ is divisible by $P_i$, and NO if it is not.
Print a newline at the end.

Sample

3
6 4 6
1
2 2 3

Yes

5
1 1 1 1 1
2
2 2 4
1 2 4

NO
Yes