Campus Design

Time Limit: 6000MS

Memory Limit: 65535KB

Description

Nanjing University of Science and Technology is celebrating its 60th anniversary. In order to make room for student activities, to make the university a more pleasant place for learning, and to beautify the campus, the college administrator decided to start construction on an open space.

The designers measured the open space and came to a conclusion that the open space is a rectangle with a length of n meters and a width of m meters. Then they split the open space into n × m squares. To make it more beautiful, the designer decides to cover the open space with 1 × 1 bricks and 1 × 2 bricks, according to the following rules:

1. All the bricks can be placed horizontally or vertically

2. The vertexes of the bricks should be placed on integer lattice points

3. The number of 1 × 1 bricks shouldn’t be less than C or more than D. The number of

    1 × 2 bricks is unlimited.

4. Some squares have a flowerbed on it, so it should not be covered by any brick. (We use 0 to represent a square with     flowerbed and 1 to represent other squares)

Now the designers want to know how many ways are there to cover the open space, meeting the above requirements.


Input

There are several test cases, please process till EOF.

Each test case starts with a line containing four integers N (1 ≤ N ≤ 100), M (1 ≤ M ≤ 10), C, D(1 ≤ C ≤ D ≤ 20). Then following N lines, each being a string with the length of M . The string consists of ‘0’ and ‘1’ only, where ‘0’ means the square should not be covered by any brick, and ‘1’ otherwise.


Output

Please print one line per test case. Each line should contain an integers representing the answer to the problem (mod 109 + 7).


Sample Input

1 1 0 0
1
1 1 1 2
0
1 1 1 2
1
1 2 1 2
11
1 2 0 2
01
1 2 0 2
11
2 2 0 0
10
10
2 2 0 0
01
10
2 2 0 0
11
11
4 5 3 5
11111
11011
10101
11111

Sample Output

0
0
1
1
1
2
1
0
2
954

Hint

None

Source

None

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