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)

#![allow(non_snake_case)]
#![allow(dead_code)]
#![allow(unused_macros)]
#![allow(unused_imports)]

use std::str::FromStr;
use std::io::*;
use std::collections::*;
use std::cmp::*;

struct Scanner<I: Iterator<Item = char>> {
    iter: std::iter::Peekable<I>,
}

macro_rules! exit {
    () => {{
        exit!(0)
    }};
    ($code:expr) => {{
        if cfg!(local) {
            writeln!(std::io::stderr(), "===== Terminated =====")
                .expect("failed printing to stderr");
        }
        std::process::exit($code);
    }}
}

impl<I: Iterator<Item = char>> Scanner<I> {
    pub fn new(iter: I) -> Scanner<I> {
        Scanner {
            iter: iter.peekable(),
        }
    }

    pub fn safe_get_token(&mut self) -> Option<String> {
        let token = self.iter
            .by_ref()
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        if token.is_empty() {
            None
        } else {
            Some(token)
        }
    }

    pub fn token(&mut self) -> String {
        self.safe_get_token().unwrap_or_else(|| exit!())
    }

    pub fn get<T: FromStr>(&mut self) -> T {
        self.token().parse::<T>().unwrap_or_else(|_| exit!())
    }

    pub fn vec<T: FromStr>(&mut self, len: usize) -> Vec<T> {
        (0..len).map(|_| self.get()).collect()
    }

    pub fn mat<T: FromStr>(&mut self, row: usize, col: usize) -> Vec<Vec<T>> {
        (0..row).map(|_| self.vec(col)).collect()
    }

    pub fn char(&mut self) -> char {
        self.iter.next().unwrap_or_else(|| exit!())
    }

    pub fn chars(&mut self) -> Vec<char> {
        self.get::<String>().chars().collect()
    }

    pub fn mat_chars(&mut self, row: usize) -> Vec<Vec<char>> {
        (0..row).map(|_| self.chars()).collect()
    }

    pub fn line(&mut self) -> String {
        if self.peek().is_some() {
            self.iter
                .by_ref()
                .take_while(|&c| !(c == '\n' || c == '\r'))
                .collect::<String>()
        } else {
            exit!();
        }
    }

    pub fn peek(&mut self) -> Option<&char> {
        self.iter.peek()
    }
}

use std::ops::*;
use std::fmt;

#[derive(Copy, Clone, PartialEq, Debug)]
struct ModInt(usize);

const MOD: usize = 1000000007;
impl ModInt {
    fn pow(self, power: usize) -> Self {
        if power == 0 {
            return ModInt(1);
        }
        if power % 2 == 0 {
            let t = self.pow(power/2);
            return t * t;
        }
        self * self.pow(power-1)
    }

    fn inv(self) -> Self {
        self.pow(MOD - 2)
    }
}

impl Add for ModInt {
    type Output = Self;

    fn add(self, rhs: Self) -> Self {
        let mut tmp = self;
        tmp.0 += rhs.0;
        if tmp.0 >= MOD {
            tmp.0 -= MOD;
        }
        tmp
    }
}

impl AddAssign for ModInt {
    fn add_assign(&mut self, rhs: Self) {
        *self = *self + rhs;
    }
}

impl Sub for ModInt {
    type Output = Self;

    fn sub(self, rhs: Self) -> Self {
        let mut ret = self;
        if ret.0 < rhs.0 {
            ret.0 += MOD;
        }
        ret.0 -= rhs.0;
        ret
    }
}

impl SubAssign for ModInt {
    fn sub_assign(&mut self, rhs: Self) {
        *self = *self - rhs;
    }
}

impl Mul for ModInt {
    type Output = Self;

    fn mul(self, rhs: ModInt) -> Self {
        let mut ret = self;
        ret.0 *= rhs.0;
        ret.0 %= MOD;
        ret
    }
}

impl MulAssign for ModInt {
    fn mul_assign(&mut self, rhs: Self) {
        *self = *self * rhs;
    }
}

impl Div for ModInt {
    type Output = ModInt;

    fn div(self, rhs: ModInt) -> Self {
        let mut ret = self;
        ret.0 *= rhs.inv().0;
        ret.0 %= MOD;
        ret
    }
}

impl DivAssign for ModInt {
    fn div_assign(&mut self, rhs: Self) {
        *self = *self / rhs;
    }
}

impl fmt::Display for ModInt {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        write!(f, "{}", self.0)
    }
}

struct Com {
    n: usize,
    fac: Vec<ModInt>,
    finv: Vec<ModInt>,
}

impl Com {
    fn new(n: usize) -> Self {
        let mut ret = Com {
            n: n,
            fac: vec![ModInt(0); n+1],
            finv: vec![ModInt(0); n+1],
        };
        ret.com_init();
        ret
    }
    fn com_init(&mut self) {
        self.fac[0] = ModInt(1);
        if self.n > 0 {
            self.fac[1] = ModInt(1);
        }
        self.finv[0] = ModInt(1);
        for i in 2..self.n+1 {
            self.fac[i] = self.fac[i-1] * ModInt(i);
        }
        self.finv[self.n] = self.fac[self.n].inv();
        for i in (2..self.n+1).rev() {
            self.finv[i-1] = self.finv[i] * ModInt(i);
        }
    }
    fn com(&self, n: usize, k: usize) -> ModInt {
        if n < k {
            return ModInt(0);
        }
        self.fac[n] * self.finv[k] * self.finv[n - k]
    }
}

fn main() {
    let cin = stdin();
    let cin = cin.lock();
    let mut sc = Scanner::new(cin.bytes().map(|c| c.unwrap() as char));
    let K: usize = sc.get();
    let S: Vec<char> = sc.chars();
    let N = S.len();
    let com = Com::new(N+K);
    let mut ans = ModInt(0);
    for i in 0..=K {
        ans += ModInt(26).pow(K-i) * com.fac[N-1+i] * com.finv[N-1] * com.finv[i] * ModInt(25).pow(i);
    }
    println!("{}", ans);
}