CF608B Hamming Distance Sum

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| $ .

The first line of the input contains binary string $ a $ ( $ 1

Print a single integer — the sum of Hamming distances between $ a $ and all contiguous substrings of $ b $ of length $ |a| $ .

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.