Problem:
Score: 600 points

Problem Statement

How many strings can be obtained by applying the following operation on a string S exactly K times: "choose one lowercase English letter and insert it somewhere"?

The answer can be enormous, so print it modulo (10^9+7).

Constraints

K is an integer between 1 and 10^6 (inclusive).

S is a string of length between 1 and 10^6 (inclusive) consisting of lowercase English letters.

Input

Input is given from Standard Input in the following format:

K
S

Output

Print the number of strings satisfying the condition, modulo (10^9+7).

Sample Input 1

5
oof

Sample Output 1

575111451

For example, we can obtain proofend, moonwolf, and onionpuf, while we cannot obtain oofsix, oofelevennn, voxafolt, or fooooooo.

Sample Input 2

37564
whydidyoudesertme

Sample Output 2

318008117

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)


import java.io.*;
import java.util.*;

public class Main {
    private static final boolean N_CASE = false;
    private static final int MOD = 1000000007;

    private long pow(long a, int n) {
        long ret = 1;
        long base = a;
        while (n > 0) {
            if ((n & 1) > 0) {
                ret = (ret * base) % MOD;
            }
            n >>= 1;
            base = (base * base) % MOD;
        }
        return ret;
    }

    private long inv(long a) {
        return pow(a, MOD - 2);
    }

    private void solve() {
        int k = sc.nextInt();
        String s = sc.next();
        int n = s.length();
        int m = n + k;
        long ans = 0;
        long[] a = new long[m + 1];
        a[0] = a[1] = 1;
        for (int i = 2; i <= m; ++i) {
            a[i] = (a[i - 1] * i) % MOD;
        }

        for (int i = n; i <= m; ++i) {
            long v = pow(25, i - n);
            v = (v * a[i - 1]) % MOD;
            v = (v * inv(a[n - 1])) % MOD;
            v = (v * inv(a[i - n])) % MOD;
            v = (v * pow(26, m - i)) % MOD;
            ans = (ans + v) % MOD;
        }

        out.println(ans);
    }

    private void run() {
        int T = N_CASE ? sc.nextInt() : 1;
        for (int t = 0; t < T; ++t) {
            solve();
        }
    }

    private static MyWriter out;
    private static MyScanner sc;

    private static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        private MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        int[][] nextIntArray(int n, int m) {
            int[][] a = new int[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    a[i][j] = sc.nextInt();
                }
            }
            return a;
        }

        long[][] nextLongArray(int n, int m) {
            long[][] a = new long[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    a[i][j] = nextLong();
                }
            }
            return a;
        }

        List<Integer> nextList(int n) {
            List<Integer> list = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                list.add(nextInt());
            }
            return list;
        }

        List<Long> nextLongList(int n) {
            List<Long> list = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                list.add(nextLong());
            }
            return list;
        }

        char[] nextCharArray(int n) {
            return sc.next().toCharArray();
        }

        char[][] nextCharArray(int n, int m) {
            char[][] c = new char[n][m];
            for (int i = 0; i < n; i++) {
                String s = sc.next();
                for (int j = 0; j < m; j++) {
                    c[i][j] = s.charAt(j);
                }
            }
            return c;
        }
    }

    private static class MyWriter extends PrintWriter {
        private MyWriter(OutputStream outputStream) {
            super(outputStream);
        }

        void printArray(int[] a) {
            for (int i = 0; i < a.length; ++i) {
                print(a[i]);
                print(i == a.length - 1 ? '\n' : ' ');
            }
        }

        void printlnArray(int[] a) {
            for (int v : a) {
                println(v);
            }
        }

        void printList(List<Integer> list) {
            for (int i = 0; i < list.size(); ++i) {
                print(list.get(i));
                print(i == list.size() - 1 ? '\n' : ' ');
            }
        }

        void printlnList(List<Integer> list) {
            list.forEach(this::println);
        }
    }

    private <T> List<List<T>> createGraph(int n) {
        List<List<T>> g = new ArrayList<>();
        for (int i = 0; i < n; ++i) {
            g.add(new ArrayList<>());
        }
        return g;
    }

    public static void main(String[] args) {
        out = new MyWriter(new BufferedOutputStream(System.out));
        sc = new MyScanner();
        new Main().run();
        out.close();
    }
}