B'Oh no, on the first exam Madoka got this hard problem: Given integer n and m pairs of integers ( v_i, u_i ). Also there is an array b_1, b_2, ldots, b_n , initially filled with zeros. Then for each index i , where 1 <= q i <= q m , perform either b_{v_i} := b_{v_i} - 1 and b_{u_i} := b_{u_i} + 1 , or b_{v_i} := b_{v_i} + 1 and b_{u_i} := b_{u_i} - 1 . Note that exactly one of these operations should be performed for every i . Also there is an array s of length n consisting of 0 and 1 . And there is an array a_1, a_2, ldots, a_n , where it is guaranteed, that if s_i = 0 holds, then a_i = 0 . Help Madoka and determine whenever it is possible to perform operations in such way that for every i , where s_i = 1 it holds that a_i = b_i . If it possible you should also provide Madoka with a way to perform operations. The first line contains two integers n and m ( 2 <= q n <= q 10000, 1 <= q m <= q 10000 ) -- the length of the array a and the number of pair of integers. The second line contains n integers s_1, s_2, ldots s_n ( 0 <= s_i <= 1 ) -- the elements of the array s . The third line contains n integers a_1, a_2, ldots, a_n ( |a_i| <= q m ) -- the elements of the array a . It is guaranteed that if s_i = 0 holds, then a_i = 0 . i -th of the following m lines contains two integers v_i and u_i ( 1 <= q v_i, u_i <= q n, v_i ne u_i ) -- the indexes of the elements of the array b to which the operation is performed. It is also guaranteed that there are no two indices i and j , where 1 <= i < j <= m , such that (v_i, u_i) = (v_j, u_j) or (v_i, u_i) = (u_j, v_j) . In the first line print "YES" if it is possible to perform operations in the required way, and "NO" otherwise. You may print each letter in any case '...