B'Jellyfish is playing a one-player card game called "Slay the Spire". There are n cards in total numbered from 1 to n . The i -th card has power c_i . There is a binary string s of length n . If s_i = texttt{0} , the i -th card is initially in the draw pile. If s_i = texttt{1} , the i -th card is initially in Jellyfish 's hand. Jellyfish will repeat the following process until either her hand or the draw pile is empty. At the end of this process, find the probability that Jellyfish can empty the draw pile, modulo 1 ,000 ,000 ,007 . Formally, let M=1 ,000 ,000 ,007 . It can be shown that the answer can be expressed as an irreducible fraction frac{p}{q} , where p and q are integers and q not equiv 0 pmod{M} . Output the integer equal to p cdot q^{-1} bmod M . In other words, output such an integer x that 0 <= x < M and x cdot q equiv p pmod{M} . Each test contains multiple test cases. The first line contains the number of test cases t ( 1 <= q t <= q 100 ). The description of the test cases follows. The first line of each test case contains a single integer n ( 1 <= q n <= q 120 ) -- the number of cards. The second line of each test case contains n integers c_1,c_2, ldots,c_n ( 0 <= q c_i <= q n ) -- the powers of the cards. It is guaranteed that c_1 <= q c_2 <= q ldots <= q c_n . The third line of each test case contains a binary string s of length n . If s_i = texttt{0} , the i -th card is initially in the draw pile. If s_i = texttt{1} , the i -th card is initially in Jellyfish 's hand. It is guaranteed that the sum of n^2 over all test cases does not exceed 120^2 . For each test case, output the probability that Jellyfish can empty the draw pile modulo 1 ,000 ,000 ,007 . In the first test case, Jellyfish will keep playing cards with power 1$'...