Description

Dr. Yao is involved in a secret research on the topic of the properties of recurrent function. Some of the functions in this research are in the following pattern:

in which set {a_i} = {1, 2, …, d-1} and {b_i} = {0, 1, …, d-1}.
We denote:

Yao's question is that, given two positive integer m and k, could you find a minimal non-negative integer x that

Input

There are several test cases. The first line of each test case contains an integer d (2≤d≤100). The second line contains 2d-1 integers: a₁, …, a_d-1, followed by b₀, ..., b_d-1. The third line contains integer m (0<m≤10¹⁰⁰), and the forth line contains integer k (0<k≤10¹⁰⁰). The input file ends with integer -1.

Output

For each test case if it exists such an integer x, output the minimal one. We guarantee the answer is less than 2⁶³. Otherwise output a word "NO".

2
1
1 0
4
7
2
1
0 1
100
200
-1

1
NO

Hint

For the first sample case, we can see that f(4)=7. And for the second one, the function is f(i)=i.

Source

POJ Founder Monthly Contest – 2008.12.28, Yaojinyu