Problem:
Score: 400 points

Problem Statement

Amidakuji is a traditional method of lottery in Japan.

To make an amidakuji, we first draw W parallel vertical lines, and then draw horizontal lines that connect them. The length of each vertical line is H+1 [cm], and the endpoints of the horizontal lines must be at 1, 2, 3, ..., or H [cm] from the top of a vertical line.

A valid amidakuji is an amidakuji that satisfies the following conditions:

No two horizontal lines share an endpoint.

The two endpoints of each horizontal lines must be at the same height.

A horizontal line must connect adjacent vertical lines.

Find the number of the valid amidakuji that satisfy the following condition, modulo 1\ 000\ 000\ 007: if we trace the path from the top of the leftmost vertical line to the bottom, always following horizontal lines when we encounter them, we reach the bottom of the K-th vertical line from the left.

For example, in the following amidakuji, we will reach the bottom of the fourth vertical line from the left.

Constraints

H is an integer between 1 and 100 (inclusive).

W is an integer between 1 and 8 (inclusive).

K is an integer between 1 and W (inclusive).

Input

Input is given from Standard Input in the following format:

H W K

Output

Print the number of the amidakuji that satisfy the condition, modulo 1\ 000\ 000\ 007.

Sample Input 1

1 3 2

Sample Output 1

1

Only the following one amidakuji satisfies the condition:

Sample Input 2

1 3 1

Sample Output 2

2

Only the following two amidakuji satisfy the condition:

Sample Input 3

2 3 3

Sample Output 3

1

Only the following one amidakuji satisfies the condition:

Sample Input 4

2 3 1

Sample Output 4

5

Only the following five amidakuji satisfy the condition:

Sample Input 5

7 1 1

Sample Output 5

1

As there is only one vertical line, we cannot draw any horizontal lines. Thus, there is only one amidakuji that satisfies the condition: the amidakuji with no horizontal lines.

Sample Input 6

15 8 5

Sample Output 6

437760187

Be sure to print the answer modulo 1\ 000\ 000\ 007.

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

a,b,c=map(int,input().split())
s=[[0]*b for i in range(a+1)]
s[0][0]=1
k=[[1,1,1],[2,1,1,1,2],[3,2,2,1,2,2,3],[5,3,3,2,4,2,3,3,5],[8,5,5,3,6,4,6,3,5,5,8],[13,8,8,5,10,6,9,6,10,5,8,8,13],[21,13,13,8,16,10,15,9,15,10,16,8,13,13,21]]
if b==1:
    print(1)
elif c-a>=2:
    print(0)    
else:
    d=k[b-2]
    for i in range(1,a+1):
        s[i][b-1]=s[i-1][b-1]*d[2*(b-1)]+s[i-1][b-2]*d[2*(b-1)-1]
        for j in range(0,b-1):
            if j==0:
                s[i][0]=s[i-1][0]*d[0]+s[i-1][1]*d[1]
            else:    
                s[i][j]=s[i-1][j-1]*d[2*j-1]+s[i-1][j]*d[2*j]+s[i-1][j+1]*d[2*j+1]
print(s[a][c-1]%(10**9+7))