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 Rust (1.42.0) (judge verdict: Accepted)

fn main() {
    proconio::input! {
        k: usize,
        s: String,
    }
    let n=s.as_bytes().len();
    let mut a=0;
    let mut c=1;
    for i in n..=n+k {
        let t=c*f(25,i-n)%MOD*f(26,n+k-i)%MOD;
        a=(a+t)%MOD;
        c=c*i%MOD*f(i-n+1,MOD-2)%MOD;
    }
    println!("{}",a);
}
const MOD: usize=1000000007;
fn f(mut i: usize, mut n: usize) -> usize {
    let mut x=1;
    while n>0 {
        if n&1==1 {
            x=x*i%MOD;
        }
        i=i*i%MOD;
        n>>=1;
    }
    x
}