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)

h,w,k = map(int, input().split())
mod = 10**9+7

dp = [[0]*w for _ in range(h+1)]

dp[0][0] = 1

onerow_t = [0]*(w-1) # i番目の横棒があるような1行の線の引き方の場合の数

for i in range(1<<(w-1)):
    tf = [None]*(w-1)
    valid = True
    for d in range(w-1):
        if (i>>d)&1 != 0:
            tf[d] = True
        if d>0 and tf[d-1] and tf[d]:
            valid = False
            break
    # print(bin(i), tf, valid)
    if valid:
        for d in range(w-1):
            if tf[d]:
                onerow_t[d] += 1

onerow_sum = sum(onerow_t)+1

for i in range(1,h+1):
    for j in range(w):
        tmp = onerow_sum
        if 0<=j-1:
            dp[i][j] += onerow_t[j-1]*dp[i-1][j-1]
            tmp -= onerow_t[j-1]
        if j+1<w:
            dp[i][j] += onerow_t[j]*dp[i-1][j+1]
            tmp -= onerow_t[j]
        # print('i,j,tmp',i,j,tmp)
        dp[i][j] += tmp*dp[i-1][j]
        dp[i][j] = dp[i][j]%mod

# print(onerow_t)
# print(dp)
print(dp[h][k-1])