T = input()
K = int(input())

MOD = 10**9+7

def matrix(a, b):
    ans = [[0]*len(b[0]) for _ in range(len(a))]
    for i in range(len(a)):
        for j in range(len(b[0])):
            ans[i][j] = sum(a[i][k]*b[k][j]%MOD for k in range(len(b)))%MOD
    return ans

M = [[]]
N = len(T)
for n in range(7):
    dp = [[0]*7 for _ in range(N+1)]
    dp[0][n] = 1
    for i in range(N):
        for j in range(7):
            dp[i+1][j] += dp[i][j]
            dp[i+1][j] %= MOD
        if T[i] == "0":
            dp[i+1][0] += dp[i][1]+dp[i][6]
            dp[i+1][0] %= MOD
            dp[i+1][2] += dp[i][3]+dp[i][1]+dp[i][6]
            dp[i+1][2] %= MOD
            dp[i+1][4] += dp[i][5]+2*dp[i][3]+dp[i][1]+dp[i][6]
            dp[i+1][4] %= MOD
        else:
            dp[i+1][1] += dp[i][0]+dp[i][6]
            dp[i+1][1] %= MOD
            dp[i+1][3] += dp[i][2]+dp[i][0]+dp[i][6]
            dp[i+1][3] %= MOD
            dp[i+1][5] += dp[i][4]+2*dp[i][2]+dp[i][0]+dp[i][6]
            dp[i+1][5] %= MOD
    M[0].append(dp[-1])
M[0] = list(map(list, zip(*M[0])))
for _ in range(59):
    M.append(matrix(M[-1], M[-1]))

ansM = [[0] for _ in range(7)]
ansM[-1][0] = 1
for i in range(60):
    if 1<<i & K:
        ansM = matrix(M[i], ansM)

print((ansM[4][0]+ansM[5][0])%MOD)