// Go in my style.
// Not afraid to dark.

#include <bits/stdc++.h>
using namespace std;

clock_t sttime;
#define STCLOCK sttime = clock ();
#define TIMENOW fprintf (stderr, "\nNOW TIME COSSEMED: %0.4lf\n", 1.0 * (clock () - sttime) / CLOCKS_PER_SEC);
#define inline __inline__ __attribute__ ((always_inline))

namespace io {
    int read_pos, read_dt; char read_char;
    inline int read (int &p = read_pos){
        p = 0, read_dt = 1; read_char = getchar ();
        while (! isdigit (read_char)){
            if (read_char == '-')
                read_dt = - 1;
            read_char = getchar ();
        }
        while (isdigit (read_char)){
            p = (p << 1) + (p << 3) + read_char - 48;
            read_char = getchar ();
        }
        return p = p * read_dt;
    }
    int write_sta[65], write_top;
    inline void write (int x){
        if (x < 0)
            putchar ('-'), x = - x;
        write_top = 0;
        do
            write_sta[write_top ++] = x % 10, x /= 10;
        while (x);
        while (write_top)
            putchar (write_sta[-- write_top] + 48);
    }
    inline int next_blank (){
        static char c; c = getchar ();
        while (! isdigit (c)) c = getchar ();
        return c - 48
;    }
}

const int N = 5e6, mod = 1e9 + 7;
int n, m, a[N + 5], f[N + 5][11][2];
long long jc[25], inv[25], inj[25];

inline int MOD (int x){ return x >= mod ? x - mod : x; }
inline int C (int x, int y){ return jc[x] * inj[y] % mod * inj[x - y] % mod; }

signed main (){
    STCLOCK

    io::read (n), io::read (m);
    for (int i = 1;i <= n;++ i) a[i] = io::next_blank ();
    f[n + 1][0][0] = f[n + 1][0][1] = 1;
    for (int i = n;i >= 1;-- i){
        f[i][0][0] = f[i][0][1] = 1;
        if ((i << 1) > n && ! a[i]) f[i][1][1] = 1;
        if (! (i & 1)){
            int x, y;
            for (int j = 0;j <= m;++ j){
                x = y = 0;
                for (int k = 0;k <= j;++ k)
                    x = (x + 1ll * f[i][k][1] * f[i + 1][j - k][1]) % mod,
                    y = (y + 1ll * f[i][k][0] * f[i + 1][j - k][0]) % mod;
                f[i >> 1][j][0] = x;
                f[i >> 1][j][1] = MOD (f[i >> 1][j][1] + x);
                if (j < m && ! a[i >> 1]) f[i >> 1][j + 1][1] = y;
            }
        }
    }
    jc[0] = jc[1] = inv[1] = inj[0] = inj[1] = 1;
    for (int i = 2;i <= (m << 1);++ i){
        inv[i] = inv[i - mod % i] * (mod / i + 1) % mod;
        jc[i] = jc[i - 1] * i % mod;
        inj[i] = inj[i - 1] * inv[i] % mod;
    }
    int ans = 0;
    for (int i = 1;i <= m;++ i)
        ans = (ans + 1ll * f[1][i][1] * C (m - 1, i - 1)) % mod;
    io::write (ans), putchar ('\n');

    TIMENOW
    return 0;
}