H. Self-exploration
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Being bored of exploring the Moon over and over again Wall-B decided to explore something he is made of — binary numbers. He took a binary number and decided to count how many times different substrings of length two appeared. He stored those values in $$$c_{00}$$$, $$$c_{01}$$$, $$$c_{10}$$$ and $$$c_{11}$$$, representing how many times substrings 00, 01, 10 and 11 appear in the number respectively. For example:

$$$10111100 \rightarrow c_{00} = 1, \ c_{01} = 1,\ c_{10} = 2,\ c_{11} = 3$$$

$$$10000 \rightarrow c_{00} = 3,\ c_{01} = 0,\ c_{10} = 1,\ c_{11} = 0$$$

$$$10101001 \rightarrow c_{00} = 1,\ c_{01} = 3,\ c_{10} = 3,\ c_{11} = 0$$$

$$$1 \rightarrow c_{00} = 0,\ c_{01} = 0,\ c_{10} = 0,\ c_{11} = 0$$$

Wall-B noticed that there can be multiple binary numbers satisfying the same $$$c_{00}$$$, $$$c_{01}$$$, $$$c_{10}$$$ and $$$c_{11}$$$ constraints. Because of that he wanted to count how many binary numbers satisfy the constraints $$$c_{xy}$$$ given the interval $$$[A, B]$$$. Unfortunately, his processing power wasn't strong enough to handle large intervals he was curious about. Can you help him? Since this number can be large print it modulo $$$10^9 + 7$$$.

Input

First two lines contain two positive binary numbers $$$A$$$ and $$$B$$$ ($$$1 \leq A \leq B < 2^{100\,000}$$$), representing the start and the end of the interval respectively. Binary numbers $$$A$$$ and $$$B$$$ have no leading zeroes.

Next four lines contain decimal numbers $$$c_{00}$$$, $$$c_{01}$$$, $$$c_{10}$$$ and $$$c_{11}$$$ ($$$0 \leq c_{00}, c_{01}, c_{10}, c_{11} \leq 100\,000$$$) representing the count of two-digit substrings 00, 01, 10 and 11 respectively.

Output

Output one integer number representing how many binary numbers in the interval $$$[A, B]$$$ satisfy the constraints mod $$$10^9 + 7$$$.

Examples
Input
10
1001
0
0
1
1
Output
1
Input
10
10001
1
2
3
4
Output
0
Note

Example 1: The binary numbers in the interval $$$[10,1001]$$$ are $$$10,11,100,101,110,111,1000,1001$$$. Only number 110 satisfies the constraints: $$$c_{00} = 0, c_{01} = 0, c_{10} = 1, c_{11} = 1$$$.

Example 2: No number in the interval satisfies the constraints