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 PyPy2 (7.3.0) (judge verdict: Runtime Error)

MOD = 10 ** 9 + 7
K = int(input())
M = len(input())
N = M + K

pow25 = [1] * (N + 1)
fac = [1] * (N + 1)
inv = [1] * (N + 1)
for x in range(1, N + 1):
    fac[x] = fac[x - 1] * x % MOD
    pow25[x] = pow25[x - 1] * 25 % MOD
inv[N] = pow(fac[N], MOD-2, MOD)
for x in range(N - 1, -1, -1):
    inv[x] = inv[x + 1] * (x + 1) % MOD

def binom(n, k):
    return fac[n] * inv[n - k] % MOD * inv[k] % MOD

ans = 0
for k in range(M, N + 1):
    ans += binom(N, k) * pow25[N - k] % MOD
    ans %= MOD
print(ans)