CF1687C 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).

Test case 1: One possible way of turning $ a $ to $ b $ : First, select $ [1,3] $ . After the operation, $ a=[3,2,5,2,3] $ . Then, select $ [2,5] $ . After the operation, $ a=[3,2,5,4,1]=b $ . Test case 2: It can be shown that it is impossible to turn $ a $ into $ b $ .