Furik loves writing all sorts of problems, especially such that he can't solve himself. You've got one of his problems, the one Furik gave to Rubik. And Rubik asks you to solve it.

There is integer n and array a, consisting of ten integers, indexed by numbers from 0 to 9. Your task is to count the number of positive integers with the following properties:

  * the number's length does not exceed n; 
  * the number doesn't have leading zeroes; 
  * digit i (0 ≤ i ≤ 9) occurs in the number at least a[i] times. 

Input

The first line contains integer n (1 ≤ n ≤ 100). The next line contains 10 integers a[0], a[1], ..., a[9] (0 ≤ a[i] ≤ 100) — elements of array a. The numbers are separated by spaces.

Output

On a single line print the remainder of dividing the answer to the problem by 1000000007 (109 + 7).

Examples

Input

1
0 0 0 0 0 0 0 0 0 1


Output

1


Input

2
1 1 0 0 0 0 0 0 0 0


Output

1


Input

3
1 1 0 0 0 0 0 0 0 0


Output

36

Note

In the first sample number 9 meets the requirements.

In the second sample number 10 meets the requirements.

In the third sample numbers 10, 110, 210, 120, 103 meet the requirements. There are other suitable numbers, 36 in total.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.FilterInputStream;
import java.io.BufferedInputStream;
import java.io.InputStream;

/**
 * @author khokharnikunj8
 */

public class Main {
    public static void main(String[] args) {
        new Thread(null, new Runnable() {
            public void run() {
                new Main().solve();
            }
        }, "1", 1 << 26).start();
    }

    void solve() {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        ScanReader in = new ScanReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BNumbers solver = new BNumbers();
        solver.solve(1, in, out);
        out.close();
    }

    static class BNumbers {
        int mod = 1000000007;

        public void solve(int testNumber, ScanReader in, PrintWriter out) {
            int n = in.scanInt();
            int[] ar = new int[10];
            for (int i = 0; i < 10; i++) {
                ar[i] = in.scanInt();
            }
            int[][] nCr = new int[101][];
            for (int i = 0; i <= 100; i++) {
                nCr[i] = new int[i + 2];
                for (int j = 0; j <= i; j++) {
                    if (i == 0 || j == 0) nCr[i][j] = 1;
                    else nCr[i][j] = (nCr[i - 1][j - 1] + nCr[i - 1][j]) % mod;
                }
            }
            long ans = 0;
            for (int i = 1; i <= 9; i++) {
                ar[i]--;
                long[][] dp = new long[2][n];
                dp[1][0] = 1;
                for (int j = 0; j <= 9; j++) {
                    Arrays.fill(dp[j & 1], 0);
                    for (int k = 0; k < n; k++) {
                        for (int l = Math.max(0, ar[j]); k + l < n; l++) {
                            dp[j & 1][k + l] = (dp[j & 1][k + l] + dp[(j - 1) & 1][k] * nCr[k + l][l]) % mod;
                        }
                    }
                }
                for (int j = 0; j < n; j++) ans = (ans + dp[1][j]) % mod;
                ar[i]++;
            }
            out.println(ans);


        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int index;
        private BufferedInputStream in;
        private int total;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (index >= total) {
                index = 0;
                try {
                    total = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (total <= 0) return -1;
            }
            return buf[index++];
        }

        public int scanInt() {
            int integer = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    integer *= 10;
                    integer += n - '0';
                    n = scan();
                }
            }
            return neg * integer;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

    }
}

