Ancient Egyptians are known to have used a large set of symbols to write on the walls of the temples. Fafa and Fifa went to one of the temples and found two non-empty words S₁ and S₂ of equal lengths on the wall of temple written one below the other. Since this temple is very ancient, some symbols from the words were erased. The symbols in the set have equal probability for being in the position of any erased symbol.

Fifa challenged Fafa to calculate the probability that S₁ is lexicographically greater than S₂. Can you help Fafa with this task?

You know that , i. e. there were m distinct characters in Egyptians' alphabet, in this problem these characters are denoted by integers from 1 to m in alphabet order. A word x is lexicographically greater than a word y of the same length, if the words are same up to some position, and then the word x has a larger character, than the word y.

We can prove that the probability equals to some fraction , where P and Q are coprime integers, and . Print as the answer the value , i. e. such a non-negative integer less than 10⁹ + 7, such that , where means that a and b give the same remainders when divided by m.

The first line contains two integers n and m (1 ≤ n,  m ≤ 10⁵) — the length of each of the two words and the size of the alphabet , respectively.

The second line contains n integers a₁, a₂, ..., a_n (0 ≤ a_i ≤ m) — the symbols of S₁. If a_i = 0, then the symbol at position i was erased.

The third line contains n integers representing S₂ with the same format as S₁.

Print the value , where P and Q are coprime and is the answer to the problem.