write a go solution for Description:
There are n bags numbered from 1 to n, the i-th bag contains a_i golden coins and b_i silver coins.

The value of a gold coin is 1. The value of a silver coin is either 0 or 1, determined for each silver coin independently (0 with probability 1/2, 1 with probability 1/2).

You have to answer q independent queries. Each query is the following:

- l r — calculate the probability that the total value of coins in bags from l to r is strictly greater than the total value in all other bags.

Input Format:
The first line contains two integers n and q (1<=n,q<=3*10^5) — the number of bags and the number of queries, respectively.

The second line contains n integers a_1,a_2,...,a_n (0<=a_i<=10^6) — the number of gold coins in the i-th bag.

The third line contains n integers b_1,b_2,...,b_n (0<=b_i<=10^6) — the number of silver coins in the i-th bag.

Next q lines contain queries. The j-th of the next q lines contains two integers l_j and r_j (1<=l_j<=r_j<=n) — the description of the j-th query.

Additional constraints on the input:

- the sum of the array a doesn't exceed 10^6;
- the sum of the array b doesn't exceed 10^6.

Output Format:
For each query, print one integer — the probability that the total value of coins in bags from l to r is strictly greater than the total value in all other bags, taken modulo 998244353.

Formally, the probability can be expressed as an irreducible fraction x/y. You have to print the value of x*y^-1bmod998244353, where y^-1 is an integer such that y*y^-1bmod998244353=1.

Note:
In both queries from the first example, the answer is 1/4.. Output only the code with no comments, explanation, or additional text.