A15112 | Sanae and Giant Robot

Is it really?! The robot only existing in my imagination?! The Colossal Walking Robot?!!

— Kochiya Sanae



Sanae made a giant robot — Hisoutensoku, but something is wrong with it. To make matters worse, Sanae can not figure out how to stop it, and she is forced to fix it on-the-fly.The state of a robot can be represented by an array of integers of length $n$ . Initially, the robot is at state $a$ . She wishes to turn it into state $b$ .

As a great programmer, Sanae knows the art of copy-and-paste. In one operation, she can choose some segment from given segments, copy the segment from $b$ and paste it into the same place of the robot, replacing the original state there. However, she has to ensure that the sum of $a$ does not change after each copy operation in case the robot go haywire. Formally, Sanae can choose segment $[l,r]$ and assign $a_i = b_i$ ( $l\le i\le r$ ) if $\sum\limits_{i=1}^n a_i$ does not change after the operation.

Determine whether it is possible for Sanae to successfully turn the robot from the initial state $a$ to the desired state $b$ with any (possibly, zero) operations.

Each test contains multiple test cases. The first line contains a single integer $t$ ( $1 \leq t \leq 2\cdot 10^4$ ) — the number of test cases. The descriptions of the test cases follow.

The first line of each test case contains two integers $n$ , $m$ ( $2 \leq n\leq 2\cdot 10^5$ , $1 \leq m\leq 2\cdot 10^5$ ) — the length of $a$ , $b$ and the number of segments.

The second line contains $n$ intergers $a_1,a_2,\ldots,a_n$ ( $1 \leq a_i \leq 10^9$ ) — the initial state $a$ .

The third line contains $n$ intergers $b_1,b_2,\ldots,b_n$ ( $1 \leq b_i \leq 10^9$ ) — the desired state $b$ .

Then $m$ lines follow, the $i$ -th line contains two intergers $l_i,r_i$ ( $1 \leq l_i < r_i \leq n$ ) — the segments that can be copy-pasted by Sanae.

It is guaranteed that both the sum of $n$ and the sum of $m$ over all test cases does not exceed $2 \cdot 10 ^ 5$ .

For each test case, print "YES" (without quotes) if $a$ can be turned into $b$ , or "NO" (without quotes) otherwise.

You can output "YES" and "NO" in any case (for example, strings "yEs", "yes" and "Yes" will be recognized as a positive response).