Genos needs your help. He was asked to solve the following programming problem by Saitama: The length of some string s is denoted s. The Hamming distance between two strings s and t of equal length is defined as , where s i is the i -th character of s and t i is the i -th character of t . For example, the Hamming distance between string "0011" and string "0110" is 0 - 0 + 0 - 1 + 1 - 1 + 1 - 0 = 0 + 1 + 0 + 1 = 2. Given two binary strings a and b , find the sum of the Hamming distances between a and all contiguous substrings of b of length a.
输入描述:
The first line of the input contains binary string a (1 ≤ a ≤ 200 000).The second line of the input contains binary string b (a ≤ b ≤ 200 000).Both strings are guaranteed to consist of characters '0' and '1' only.
输出描述:
Print a single integer — the sum of Hamming distances between a and all contiguous substrings of b of length a.
示例1
输入
01<br />00111<br />0011<br />0110<br />
备注:
For the first sample case, there are four contiguous substrings of b of length a: "00", "01", "11", and "11". The distance between "01" and "00" is 0 - 0 + 1 - 0 = 1. The distance between "01" and "01" is 0 - 0 + 1 - 1 = 0. The distance between "01" and "11" is 0 - 1 + 1 - 1 = 1. Last distance counts twice, as there are two occurrences of string "11". The sum of these edit distances is 1 + 0 + 1 + 1 = 3.The second sample case is described in the statement.
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