535_D. Tavas and Malekas_34957
Tavas is a strange creature. Usually "zzz" comes out of people's mouth while sleeping, but string s of length n comes out from Tavas' mouth instead.

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Today Tavas fell asleep in Malekas' place. While he was sleeping, Malekas did a little process on s. Malekas has a favorite string p. He determined all positions x1 < x2 < ... < xk where p matches s. More formally, for each xi (1 ≤ i ≤ k) he condition sxisxi + 1... sxi + |p| - 1 = p is fullfilled.

Then Malekas wrote down one of subsequences of x1, x2, ... xk (possibly, he didn't write anything) on a piece of paper. Here a sequence b is a subsequence of sequence a if and only if we can turn a into b by removing some of its elements (maybe no one of them or all).

After Tavas woke up, Malekas told him everything. He couldn't remember string s, but he knew that both p and s only contains lowercase English letters and also he had the subsequence he had written on that piece of paper.

Tavas wonders, what is the number of possible values of s? He asked SaDDas, but he wasn't smart enough to solve this. So, Tavas asked you to calculate this number for him.

Answer can be very large, so Tavas wants you to print the answer modulo 109 + 7.

Input

The first line contains two integers n and m, the length of s and the length of the subsequence Malekas wrote down (1 ≤ n ≤ 106 and 0 ≤ m ≤ n - |p| + 1).

The second line contains string p (1 ≤ |p| ≤ n).

The next line contains m space separated integers y1, y2, ..., ym, Malekas' subsequence (1 ≤ y1 < y2 < ... < ym ≤ n - |p| + 1).

Output

In a single line print the answer modulo 1000 000 007.

Examples

Input

6 2
ioi
1 3


Output

26


Input

5 2
ioi
1 2


Output

0

Note

In the first sample test all strings of form "ioioi?" where the question mark replaces arbitrary English letter satisfy.

Here |x| denotes the length of string x.

Please note that it's possible that there is no such string (answer is 0).
import java.io.*;
import java.util.*;
import java.util.zip.ZipEntry;
import java.math.*;

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Input in = new Input(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(1, in, out);
        out.close();
    }
}

class Task {
    static final long MOD = 1000000007;
    int[] primes;

    public void solve(int testNumber, Input in, PrintWriter out) {
        int n = in.nextInt();
        int m = in.nextInt();
        char[] p = in.next().toCharArray();
        int[] y = new int[m];
        for (int i = 0; i < m; i++) {
            y[i] = in.nextInt();
        }
        char[] s = new char[n + 1];
        Arrays.fill(s, '?');
        int len = p.length;

        Set<Long> magicSet = new HashSet<>();
        long[] cof = new long[len];
        cof[0] = 1;
        for (int i = 1; i < len; i++) {
            cof[i] = cof[i - 1] * 33 % MOD;
        }
        long hashCode = 0;
        long[] hash = new long[len];
        for (int i = 0; i < len; i++) {
            hashCode = (hashCode + (p[i] - 'a' + 1) * cof[i]) % MOD;
            hash[i] = hashCode;
            magicSet.add(hashCode);
        }
        long miss = 0;
        if (m > 0) {
            miss = y[0] - 1;
            miss += n - (y[m - 1] + len - 1);
        } else {
            miss = n;
        }

        for (int i = 0; i < m - 1; i++) {
            int t = (y[i] + len - 1) - y[i + 1];
            if (t >= 0) {
                long h = hash[len - 1] - hash[len - t - 2];
                while (h < 0)
                    h += MOD;
                h *= ModInverse(cof[len - t - 1]);
                h %= MOD;
                if (!magicSet.contains(h)) {
                    out.println(0);
                    return;
                }
            } else {
                miss += y[i + 1] - (y[i] + len);
            }
        }
        long ans = 1L;
        for (int i = 0; i < miss; i++) {
            ans = ans * 26 % MOD;
        }
        out.println(ans);
    }

    private boolean isQuare(int[][] m) {
        long[] dist = new long[6];
        int index = 0;
        for (int i = 0; i < 4; i++) {
            for (int j = i + 1; j < 4; j++) {
                dist[index++] = dist(m[i][0], m[i][1], m[j][0], m[j][1]);
            }
        }
        Arrays.sort(dist);
        if (dist[0] == 0 || dist[5] == 0)
            return false;
        for (int i = 0; i < 2; i++) {
            if (dist[i] != dist[i + 1])
                return false;
        }

        return dist[4] == dist[5];
    }

    private long dist(long x1, long y1, long x2, long y2) {
        return (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
    }

    static void rotate(int[][] m, int row) {
        int x = m[row][0] - m[row][2];
        int y = m[row][1] - m[row][3];
        m[row][0] = m[row][2] - y;
        m[row][1] = m[row][3] + x;
    }

    // didn't test
    static class BIT {
        int[] MAX;
        int[] MIN;
        int[] SUM;
        int n;

        public BIT(int n) {
            MAX = new int[n + 1];
            MIN = new int[n + 1];
            SUM = new int[n + 1];
            this.n = n;
        }

        public void setSum(int pos, int val) {
            for (int i = pos; i < n; i += (i & -i)) {
                SUM[i] += val;
            }
        }

        public int getSum(int to) {
            int sum = 0;
            for (int i = to; i > 0; i -= (i & -i)) {
                sum += SUM[i];
            }
            return sum;
        }

        public int getSum(int from, int to) {
            return getSum(to) - getSum(from);
        }

        public void setMax(int pos, int val) {
            for (int i = pos; i < n; i += (i & -i)) {
                MAX[i] = Math.max(val, MAX[i]);
            }
        }

        public int getMax(int to) {
            int max = 0;
            for (int i = to; i > 0; i -= (i & -i)) {
                max = Math.max(max, MAX[i]);
            }
            return max;
        }

        public void setMin(int pos, int val) {
            for (int i = pos; i < n; i += (i & -i)) {
                MIN[i] = Math.min(val, MIN[i]);
            }
        }

        public int getMin(int to) {
            int min = 0;
            for (int i = to; i > 0; i -= (i & -i)) {
                min = Math.min(min, MIN[i]);
            }
            return min;
        }

    }

    // didn't test
    static class DisjointSet {
        int[] set;

        public DisjointSet(int n) {
            set = new int[n];
            for (int i = 0; i < n; i++) {
                set[i] = i;
            }
        }

        public int findSet(int a) {
            if (set[a] == a)
                return a;
            return findSet(set[a]);
        }

        public void unionSet(int a, int b) {
            set[findSet(a)] = findSet(b);
        }

        public boolean isSameSet(int a, int b) {
            return findSet(a) == findSet(b);
        }
    }

    static class SegmentTree {
        int[] MAX;
        int[] MIN;
        int[] SUM;
        int[] data;
        int n;

        public SegmentTree(int[] data) {
            this.n = data.length;
            this.data = data;
            MAX = new int[4 * n + 10];
            MIN = new int[4 * n + 10];
            SUM = new int[4 * n + 10];
            buildTree(1, 0, n - 1);
        }

        public int left(int root) {
            return root << 1;
        }

        public int right(int root) {
            return (root << 1) + 1;
        }

        private void buildTree(int root, int rl, int rr) {
            if (rr == rl) {
                MAX[root] = MIN[root] = SUM[root] = data[rr];
            } else {
                int rm = (rl + rr) >> 1;
                buildTree(left(root), rl, rm);
                buildTree(right(root), rm + 1, rr);
                MAX[root] = Math.max(MAX[left(root)], MAX[right(root)]);
                MIN[root] = Math.min(MIN[left(root)], MIN[right(root)]);
                SUM[root] = SUM[left(root)] + SUM[right(root)];
            }
        }

        public int getMax(int from, int to) {
            return getMax(1, 0, n - 1, from, to);
        }

        private int getMax(int root, int rl, int rr, int from, int to) {
            if (from > rr || to < rl || rl > rr) {
                return -1;
            }
            if (from == rl && to == rr) {
                return MAX[root];
            }
            int rm = (rr + rl) >> 1;
            int m1 = getMax(left(root), rl, rm, from, Math.min(to, rm));
            int m2 = getMax(right(root), rm + 1, rr, Math.max(from, rm + 1), to);
            return Math.max(m1, m2);
        }

        public int getMin(int from, int to) {
            return getMin(1, 0, n - 1, from, to);
        }

        private int getMin(int root, int rl, int rr, int from, int to) {
            if (from > rr || to < rl || rl > rr) {
                return Integer.MAX_VALUE;
            }
            if (from == rl && to == rr) {
                return MIN[root];
            }
            int rm = (rr + rl) >> 1;
            int m1 = getMin(left(root), rl, rm, from, Math.min(to, rm));
            int m2 = getMin(right(root), rm + 1, rr, Math.max(from, rm + 1), to);
            return Math.min(m1, m2);
        }

        public int getSum(int from, int to) {
            return getSum(1, 0, n - 1, from, to);
        }

        private int getSum(int root, int rl, int rr, int from, int to) {
            if (from > rr || to < rl || rl > rr) {
                return 0;
            }
            if (from == rl && to == rr) {
                return SUM[root];
            }
            int rm = (rr + rl) >> 1;
            int m1 = getSum(left(root), rl, rm, from, Math.min(to, rm));
            int m2 = getSum(right(root), rm + 1, rr, Math.max(from, rm + 1), to);
            return m1 + m2;
        }
    }

    private String lcs(String s1, String s2) {
        int n = s1.length();
        int m = s2.length();
        int[][] dp = new int[n + 1][m + 1];
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= m; j++) {
                if (s1.charAt(i - 1) == s2.charAt(j - 1)) {
                    dp[i][j] = dp[i - 1][j - 1] + 1;
                } else {
                    dp[i][j] = Math.max(dp[i - 1][j], dp[i][j - 1]);
                }
            }
        }
        StringBuilder sb = new StringBuilder();
        int i = n;
        int j = m;
        while (i > 0 && j > 0) {
            if (s1.charAt(i - 1) == s2.charAt(j - 1)) {
                sb.append(s1.charAt(i - 1));
                i--;
                j--;
            } else {
                if (dp[i - 1][j] > dp[i][j - 1]) {
                    i--;
                } else {
                    j--;
                }
            }
        }
        return sb.reverse().toString();
    }

    private boolean isPrime(int n) {
        if (n <= 3)
            return n > 1;
        else if (n % 3 == 0 || n % 2 == 0)
            return false;
        for (long i = 5; i * i <= n; i += 6) {
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
        }
        return true;
    }

    private int[] getPrimes(int n) {
        int len = n + 1;
        boolean[] isPrimes = new boolean[len];
        int[] temps = new int[len];
        int index = 0;
        Arrays.fill(isPrimes, true);
        isPrimes[0] = isPrimes[1] = false;
        for (int i = 2; i * i < len; i++) {
            if (isPrimes[i]) {
                for (int j = i * i; j < len; j += i) {
                    isPrimes[j] = false;
                }
            }
        }
        for (int i = 0; i < len; i++) {
            if (isPrimes[i])
                temps[index++] = i;
        }
        int[] primes = Arrays.copyOf(temps, index);
        return primes;
    }

    static void swap(char[] arrays, int pos1, int pos2) {
        char tmp = arrays[pos1];
        arrays[pos1] = arrays[pos2];
        arrays[pos2] = tmp;
    }

    static void swap(int[] arrays, int pos1, int pos2) {
        int tmp = arrays[pos1];
        arrays[pos1] = arrays[pos2];
        arrays[pos2] = tmp;
    }

    static long modPow(long n, long ex) {
        long res = 1;
        while (ex > 0) {
            if ((ex & 1) == 1)
                res = res * n % MOD;
            n = n * n % MOD;
            ex >>= 1;
        }
        return res;
    }

    static long ModInverse(long n) {
        return modPow(n, MOD - 2);
    }

    static long nCr(int n, int r) {
        if (r > n)
            return -1;
        // return (f[n] * ModInverse((f[r] * f[n - r]) % MOD)) % MOD;
        return 0;
    }
}

class Input {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public Input(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }
}
