There are $n$ shops numbered with successive integers from $1$ to $n$ in Byteland. Every shop sells only one kind of goods, and the price of the $i$-th shop's goods is $v_i$. The distance between the $i$-th shop and Byteasar's home is $d_i$.
Every day, Byteasar will purchase some goods. On the $i$-th day, he will choose an interval $[l_i,r_i]$ and an upper limit $c_i$. Then, he will visit each shop with distance at most $c_i$ away from home in $[l_i,r_i]$, buy at most one piece of goods from each shop and go back home. Of course, he can also choose to buy nothing. Back home, Byteasar will calculate the total amount of money he has costed that day and write it down on his account book, denoted as $sum_i$.
However, due to Byteasar's poor math, he may calculate it wrong.
Please write a program to help Byteasar judge whether each number is sure to be calculated wrong.
Input
The first line of the input contains an integer $T$ $(1\leq T\leq 10)$, denoting the number of test cases.
In each test case, the first line of the input contains two integers $n,m$ $(1\leq n\leq 20000,1\leq m\leq 100000)$, denoting the number of shops and the number of records on Byteasar's account book.
The second line of the input contains $n$ integers $v_1, v_2, ..., v_n$ $(1\leq v_i\leq 100)$, denoting the price of the $i$-th shop's goods.
The third line of the input contains $n$ integers $d_1, d_2, ..., d_n$ $(1\leq d_i\leq 10^9)$, denoting the distance between the $i$-th shop and Byteasar's home.
Each of the next $m$ lines contains four integers $l_i,r_i,c_i,sum_i$ $(1\leq l_i\leq r_i\leq n,1\leq c_i\leq 10^9,1\leq sum_i\leq 100)$, denoting a record on Byteasar's account book.
Output
For each test case, print a line with $m$ characters. If the $i$-th number is sure to be calculated wrong, then the $i$-th character should be '1'. Otherwise, it should be '0'.
