Problem: Nezzar buys his favorite snack — n chocolate bars with lengths l_1,l_2,…,l_n. However, chocolate bars might be too long to store them properly! 

In order to solve this problem, Nezzar designs an interesting process to divide them into small pieces. Firstly, Nezzar puts all his chocolate bars into a black box. Then, he will perform the following operation repeatedly until the maximum length over all chocolate bars does not exceed k.

  * Nezzar picks a chocolate bar from the box with probability proportional to its length x. 
  * After step 1, Nezzar uniformly picks a real number r ∈ (0,x) and divides the chosen chocolate bar into two chocolate bars with lengths r and x-r. 
  * Lastly, he puts those two new chocolate bars into the black box. 



Nezzar now wonders, what is the expected number of operations he will perform to divide his chocolate bars into small pieces.

It can be shown that the answer can be represented as P/Q, where P and Q are coprime integers and Q not ≡ 0 (mod 998 244 353). Print the value of P⋅ Q^{-1} mod 998 244 353.

Input

The first line contains two integers n and k (1 ≤ n ≤ 50, 1 ≤ k ≤ 2000).

The second line contains n integers l_1, l_2, …, l_n (1 ≤ l_i, ∑_{i=1}^{n} l_i ≤ 2000).

Output

Print a single integer — the expected number of operations Nezzar will perform to divide his chocolate bars into small pieces modulo 998 244 353.

Examples

Input


1 1
2


Output


4


Input


1 1
1


Output


0


Input


1 5
1234


Output


15630811


Input


2 1
2 3


Output


476014684


Input


10 33
10 20 30 40 50 60 70 80 90 100


Output


675105648

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;
 
/**
 * stescobedo
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        FNezzarAndChocolateBars solver = new FNezzarAndChocolateBars();
        solver.solve(1, in, out);
        out.close();
    }
 
    static class FNezzarAndChocolateBars {
        static final int MAXN = 2048;
        static final int modulo = 998244353;
 
        public int add(int x, int y) {
            x += y;
            if (x >= modulo) x -= modulo;
            return x;
        }
 
        public int subtract(int x, int y) {
            x -= y;
            if (x < 0) x += modulo;
            return x;
        }
 
        public int multiply(int x, int y) {
            return (int) ((x * 1L * y) % modulo);
        }
 
        public int power(int x, long y) {
            int ans = 1;
            for (; y > 0; y >>= 1, x = (int) ((x * 1L * x) % modulo))
                if (y % 2 == 1) ans = (int) ((ans * 1L * x) % modulo);
            return ans;
        }
 
        public int inverse(int x) {
            return power(x, modulo - 2);
        }
 
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int[] fact = new int[MAXN];
            int[] ifact = new int[MAXN];
            fact[0] = ifact[0] = 1;
            for (int i = 1; i < MAXN; i++) {
                fact[i] = multiply(fact[i - 1], i);
                ifact[i] = inverse(fact[i]);
            }
            int n = in.nextInt(), k = in.nextInt();
            int[] l = in.readIntArray(n);
            int[][][] dp = new int[2][MAXN][n + 1];
            dp[1][0][0] = 1;
            int s = 0;
 
            for (int p = 0; p < n; p++) {
                int L = l[p];
                int invL = inverse(L);
                int[] coeffs = new int[L / k + 1];
                int[] coeffs2 = new int[L / k + 1];
                for (int i = 0; i <= L / k; i++) {
                    if (k * i == L) continue;
                    int z = ifact[i];
                    if (i % 2 == 1) z = subtract(0, z);
                    coeffs[i] = multiply(z, power(L - k * i, i));
 
                    if (i >= 1) {
                        coeffs2[i] = multiply(z, multiply(i, power(L - k * i, i - 1)));
                    }
                }
                int r = p & 1;
                int h = r ^ 1;
                for (int i = 0; i <= s / k; i++) Arrays.fill(dp[r][i], 0);
                for (int i = 0; i <= s / k; i++)
                    for (int j = 0; j <= p; j++)
                        if (dp[h][i][j] != 0) {
                            int value = dp[h][i][j];
                            for (int t = 0; t <= L / k; t++) {
                                dp[r][i + t][j] = add(dp[r][i + t][j], multiply(value, coeffs[t]));
                                if (t > 0) {
                                    dp[r][i + t - 1][j + 1] = add(dp[r][i + t - 1][j + 1], multiply(value, coeffs2[t]));
                                }
                            }
                        }
                s += L;
            }
            int answer = 0;
            for (int i = 0; i <= s / k; i++)
                for (int r = 0; r <= n; r++) {
                    int value = dp[(n - 1) & 1][i][r];
                    int j = i + r;
                    if (j == 0) continue;
                    int temp = multiply(fact[i], inverse(power(k * j, i + 1)));
                    answer = add(answer, multiply(value, temp));
                }
            out.println(multiply(subtract(0, s), answer));
        }
 
    }
 
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;
 
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
 
        public int[] readIntArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++) {
                array[i] = readInt();
            }
            return array;
        }
 
        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }
 
        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }
 
        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
 
        }
 
    }
 
    static class OutputWriter {
        private final PrintWriter writer;
 
        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }
 
        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }
 
        public void println(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
            writer.print('\n');
        }
 
        public void close() {
            writer.close();
        }
 
    }
}