B

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 sᵢ is the i-th character of s and tᵢ 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|.

Input

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.

Output

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

Examples

input

01
00111

output

3

input

0011
0110

output

2

Note

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.