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 C# (Mono-csc 3.5.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

namespace Contest
{
  class Program
  {
    static void Main(string[] args)
    {
      ABC171.F();
    }
    class ABC171
    {
      public static void A()
      {
        var A = Read.Str();
        Console.WriteLine(A == A.ToLower() ? "a" : "A");
      }
      public static void B()
      {
        var N = Read.Int();
        var K = Read.Int();
        var P = Read.IntN().OrderBy(x => x).ToArray();
        Console.WriteLine(P.Take(K).Sum());
      }
      public static void C()
      {
        var N = Read.Long();
        var pow26 = new long[20];
        pow26[1] = 26;
        for(int i = 2; i < 20; ++i)
        {
          pow26[i] = pow26[i - 1] * 26;
        }
        var PS = Util.ASum(pow26);

        var x = N;
        int idx = 0;
        while (PS[idx] < N)
        {
          idx++;
        }
        var v = N - PS[idx - 1] -1;
        idx--;
        var list = new char[idx];
        for(int i = 0; i < idx; ++i)
        {
          list[idx - i - 1] = (char)('a' + (int)(v % 26));
          v /= 26;
        }
        Console.WriteLine(new string(list));
      }
      public static void D()
      {
        var N = Read.Int();
        var A = Read.LongN();
        var Q = Read.Int();
        var BC = Read.TupleInt(Q);
        var freq = Util.Frequency(A);
        long sum = A.Sum();
        var ans = new List<long>();
        foreach(var bc in BC)
        {
          var B = bc.Item1;
          var C = bc.Item2;
          if (freq.ContainsKey(B))
          {
            if (!freq.ContainsKey(C))
            {
              freq.Add(C, 0);
            }
            sum += ((long)(C - B)) * freq[B];
            freq[C] += freq[B];
            freq.Remove(B);
          }
          ans.Add(sum);
        }
        Console.WriteLine(String.Join(Environment.NewLine, ans));
      }
      public static void E()
      {
        var N = Read.Int();
        var A = Read.IntN();
        int xor = 0;
        foreach(var a in A)
        {
          xor ^= a;
        }
        Console.WriteLine(String.Join(" ", A.Select(x => x ^ xor)));
      }
      public static void F()
      {
        var K = Read.Int();
        var S = Read.Str();
        var N = K + S.Length;
        var comb = Util.Combin(N + 10, MOD.P);
        MOD ans = 0;
        MOD C26 = 25;
        for(int i = 0; i <= K; ++i)
        {
          var x = C26.Power(i) * comb(N, i);
          ans += x;
        }
        Console.WriteLine(ans.V);
      }
    }

    struct MOD
    {
      public static long P = 1000000007;
      public readonly long V;

      public MOD(long a) { this.V = a % P; }
      public static implicit operator MOD(long a) { return new MOD(a); }
      public static MOD operator +(MOD a, MOD b) { return new MOD((a.V + b.V) % P); }
      public static MOD operator -(MOD a, MOD b) { return new MOD((a.V - b.V + P) % P); }
      public static MOD operator *(MOD a, MOD b) { return new MOD((a.V * b.V) % P); }
      public static MOD operator /(MOD a, MOD b) { return new MOD((a.V * b.Inverse().V) % P); }
      public MOD Inverse()
      {
        long a = V, p = P; long b = p, c = 1, d = 0, e = 0, f = 0;
        while (b != 0) { e = a / b; f = b; b = a - e * b; a = f; f = d; d = c - e * d; c = f; }
        c %= p;
        return c + (c < 0 ? p : 0);
      }
      public MOD Power(long n)
      {
        long a = V, p = P; long res = 1; long mult = a;
        for (int i = 0; i < 63; ++i) { if ((n & ((long)1 << i)) > 0) { res = (res * mult) % p; } mult = (mult * mult) % p; }
        return res;
      }
      public override string ToString() { return V.ToString(); }
    }

    class Util
    {
      public static T[,] Gen<T>(int r, int c, T v)
      {
        var matrix = new T[r, c];
        for (int i = 0; i < r; ++i)
        {
          for (int j = 0; j < c; ++j)
          {
            matrix[i, j] = v;
          }
        }
        return matrix;
      }
      public static long[] ASum(long[] array)
      {
        var res = new long[array.Length + 1];
        for (int i = 0; i < array.Length; ++i)
        {
          res[i + 1] = res[i] + array[i];
        }
        return res;
      }
      public static long[,] ASum(long[,] matrix)
      {
        var N = matrix.GetLength(0);
        var M = matrix.GetLength(1);
        var res = new long[N + 1, M + 1];
        for(int i = 0; i < N; ++i)
        {
          for(int j = 0; j < M; ++j)
          {
            res[i + 1, j + 1] = res[i, j + 1] + res[i + 1, j] - res[i, j] + matrix[i, j];
          }
        }
        return res;
      }
      public static Dictionary<T, long> Frequency<T>(T[] array)
      {
        var dict = new Dictionary<T, long>();
        foreach (var a in array)
        {
          if (!dict.ContainsKey(a)) { dict.Add(a, 0); }
          dict[a]++;
        }
        return dict;
      }
      public static bool IsPrime(long x)
      {
        var fact = Factorize(x);
        return fact.Count == 1 && fact.Values.ElementAt(0) == 1;
      }
      public static Dictionary<long, int> Factorize(long x)
      {
        var dict = new Dictionary<long, int>();
        long minp = 2;
        while (x > 1)
        {
          bool ok = false;
          for (long p = minp; p * p <= x; ++p)
          {
            if (x % p == 0)
            {
              if (!dict.ContainsKey(p))
              {
                dict.Add(p, 0);
              }
              dict[p]++;
              minp = p;
              x /= p;
              ok = true;
              break;
            }
          }
          if (!ok)
          {
            if (!dict.ContainsKey(x)) { dict.Add(x, 0); }
            dict[x]++;
            break;
          }
        }
        return dict;
      }
      public static HashSet<int> GenPrimes(int max)
      {
        var primes = new HashSet<int>(Enumerable.Range(2, max - 1));
        for(int i = 2; i <= max; ++i)
        {
          if (primes.Contains(i))
          {
            for(int j=2; ; ++j)
            {
              if (i * j > max) { break; }
              primes.Remove(i * j);
            }
          }
        }
        return primes;
      }

      //For CombinUtil
      public static long Power(long a, long n, long p)
      {
        long res = 1;
        long mult = a;
        for (int i = 0; i < 63; ++i)
        {
          if ((n & ((long)1 << i)) > 0)
          {
            res = (res * mult) % p;
          }
          mult = (mult * mult) % p;
        }
        return res;
      }
      public static long Inverse(long a, long p)
      {
        long b = p, c = 1, d = 0, e = 0, f = 0;
        while (b != 0)
        {
          e = a / b;
          f = b; b = a - e * b; a = f;
          f = d; d = c - e * d; c = f;
        }
        c %= p;
        return c + (c < 0 ? p : 0);
      }

      public static long[] Facts(int n, long p)
      {
        var facts = new long[n + 1];
        facts[0] = 1;
        for (int i = 1; i <= n; ++i)
        {
          facts[i] = (i * facts[i - 1]) % p;
        }
        return facts;
      }
      public static Func<int, int, long> Combin(int n, long P)
      {
        var fact = Facts(n, P);
        var inv = fact.Select(x => Inverse(x, P)).ToArray();
        return (N, M) =>
        {
          if (N < 0 || N < M || M < 0) { return 0; }
          return (((fact[N] * inv[M]) % P) * inv[N - M]) % P;
        };
      }

    }

    static class Read
{
static Queue<string> queue = new Queue<string>();
static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
public static ulong[] ULongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToUInt64(s)).ToArray(); }
public static string[] StrN() { return Console.ReadLine().Split(' '); }
public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
public static long[,] LongMatrix(int r, int c) { var mat = new long[r, c]; for (int i = 0; i < r; ++i) { var x = Read.LongN(); for (int j = 0; j < c; ++j) { mat[i, j] = x[j]; } } return mat; }
public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
{
Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
        for (int i = 0; i < M; ++i) { var ab = Read.IntN(); if (!dict[ab[0]].Contains(ab[1])) { dict[ab[0]].Add(ab[1]); } if (!isDirectional && !dict[ab[1]].Contains(ab[0])) { dict[ab[1]].Add(ab[0]); } }
        return dict;
}
public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
{
Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>(); for (int i = 0; i <= N; ++i) { dict.Add(i, new Dictionary<int, long>()); }
for (int i = 0; i < M; ++i) { var ab = Read.IntN(); dict[ab[0]].Add(ab[1], ab[2]); dict[ab[1]].Add(ab[0], ab[2]); }
return dict;
}
}
    }
}