Problem Statement

You are given an integer sequence $A = (A_1, A_2, \dots, A_N)$ of length $N$. You can perform the following operation any number of times, possibly zero:

• Choose an integer pair $(i, j)$ satisfying $1 \leq i \lt j \leq N$, and replace $A_i$ with $A_i + 1$ and $A_j$ with $A_j - 1$.

Determine whether it is possible to make $A$ a non-decreasing sequence through the operations.

You are given $T$ test cases. Solve each of them.

Constraints

• $1 \leq T \leq 2 \times 10^5$
• $2 \leq N \leq 2 \times 10^5$
• $0 \leq A_i \leq 10^9$
• The sum of $N$ over all test cases is at most $2 \times 10^5$.
• All input values are integers.

Input

The input is given from Standard Input in the following format. Here, $\mathrm{case}_i$ denotes the $i$-th test case.

T
\mathrm{case}_1
\mathrm{case}_2
\vdots
\mathrm{case}_T

Each test case is given in the following format:

N
A_1 A_2 \dots A_N

Output

Print $T$ lines. The $i$-th line should contain the answer for the $i$-th test case. For each test case, if it is possible to make $A$ a non-decreasing sequence through the operations, print Yes; otherwise, print No.