ZZX has a sequence of boxes numbered $1,2,...,n$. Each box can contain at most one ball.
You are given the initial configuration of the balls. For $1 \leq i \leq n$, if the $i$-th box is empty then $a[i]=0$, otherwise the i-th box contains exactly one ball, the color of which is a[i], a positive integer. Balls with the same color cannot be distinguished.
He will perform m operations in order. At the i-th operation, he collects all the balls from boxes l[i],l[i]+1,...,r[i]-1,r[i], and then arbitrarily put them back to these boxes. (Note that each box should always contain at most one ball)
He wants to change the configuration of the balls from a[1..n] to b[1..n] (given in the same format as a[1..n]), using these operations. Please tell him whether it is possible to achieve his goal.
First line contains an integer t. Then t testcases follow. In each testcase: First line contains two integers n and m. Second line contains a,a,...,a[n]. Third line contains b,b,...,b[n]. Each of the next m lines contains two integers l[i],r[i].
1<=n<=1000,0<=m<=1000, sum of n over all testcases <=2000, sum of m over all testcases <=2000.