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(unused_imports, unused_macros, dead_code)]

macro_rules! min {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| min!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = min!($($ys),*);
        if $x < t { $x } else { t }
    }}
}
macro_rules! max {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| max!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = max!($($ys),*);
        if $x > t { $x } else { t }
    }}
}
macro_rules! ewriteln {
    ($($args:expr),*) => { let _ = writeln!(&mut std::io::stderr(), $($args),*); };
}
macro_rules! trace {
    ($x:expr) => { ewriteln!(">>> {} = {:?}", stringify!($x), $x) };
    ($($xs:expr),*) => { trace!(($($xs),*)) }
}
macro_rules! put {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        if let Some(x) = it.next() { print!("{}", x); }
        for x in it { print!(" {}", x); }
        println!("");
    }};
    ($x:expr) => { println!("{}", $x) };
    ($x:expr, $($xs:expr),*) => { print!("{} ", $x); put!($($xs),*) }
}

const M: i64 = 1_000_000_007;

#[derive(Debug, PartialEq, Eq, Clone, Copy)]
struct ModInt(i64, i64); // (residual, modulo)
impl ModInt {
    fn new(residual: i64, modulo: i64) -> ModInt {
        if residual >= modulo {
            ModInt(residual % modulo, modulo)
        } else if residual < 0 {
            ModInt((residual % modulo) + modulo, modulo)
        } else {
            ModInt(residual, modulo)
        }
    }
    fn unwrap(self) -> i64 {
        self.0
    }
    fn inv(self) -> Self {
        fn exgcd(r0: i64, a0: i64, b0: i64, r: i64, a: i64, b: i64) -> (i64, i64, i64) {
            if r > 0 {
                exgcd(r, a, b, r0 % r, a0 - r0 / r * a, b0 - r0 / r * b)
            } else {
                (a0, b0, r0)
            }
        }
        let (a, _, r) = exgcd(self.0, 1, 0, self.1, 0, 1);
        if r != 1 {
            panic!("{:?} has no inverse!", self);
        }
        ModInt(((a % self.1) + self.1) % self.1, self.1)
    }
    fn pow(self, n: i64) -> Self {
        if n < 0 {
            self.pow(-n).inv()
        } else if n == 0 {
            ModInt(1, self.1)
        } else if n == 1 {
            self
        } else {
            let mut x = (self * self).pow(n / 2);
            if n % 2 == 1 {
                x *= self
            }
            x
        }
    }
}
impl std::fmt::Display for ModInt {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}
impl std::ops::Neg for ModInt {
    type Output = Self;
    fn neg(self) -> Self {
        if self.0 == 0 {
            return self;
        }
        ModInt(self.1 - self.0, self.1)
    }
}
impl std::ops::Add<i64> for ModInt {
    type Output = Self;
    fn add(self, other: i64) -> Self {
        ModInt::new(self.0 + other, self.1)
    }
}
impl std::ops::Add for ModInt {
    type Output = Self;
    fn add(self, other: ModInt) -> Self {
        self + other.0
    }
}
impl std::ops::Add<ModInt> for i64 {
    type Output = ModInt;
    fn add(self, other: ModInt) -> ModInt {
        other + self
    }
}
impl std::ops::AddAssign<i64> for ModInt {
    fn add_assign(&mut self, other: i64) {
        self.0 = ModInt::new(self.0 + other, self.1).0;
    }
}
impl std::ops::AddAssign for ModInt {
    fn add_assign(&mut self, other: ModInt) {
        *self += other.0;
    }
}
impl std::ops::Sub<i64> for ModInt {
    type Output = Self;
    fn sub(self, other: i64) -> Self {
        ModInt::new(self.0 - other, self.1)
    }
}
impl std::ops::Sub for ModInt {
    type Output = Self;
    fn sub(self, other: ModInt) -> Self {
        self - other.0
    }
}
impl std::ops::Sub<ModInt> for i64 {
    type Output = ModInt;
    fn sub(self, other: ModInt) -> ModInt {
        ModInt::new(self - other.0, other.1)
    }
}
impl std::ops::SubAssign<i64> for ModInt {
    fn sub_assign(&mut self, other: i64) {
        self.0 = ModInt::new(self.0 - other, self.1).0;
    }
}
impl std::ops::SubAssign for ModInt {
    fn sub_assign(&mut self, other: ModInt) {
        *self -= other.0;
    }
}
impl std::ops::Mul<i64> for ModInt {
    type Output = Self;
    fn mul(self, other: i64) -> Self {
        ModInt::new(self.0 * other, self.1)
    }
}
impl std::ops::Mul for ModInt {
    type Output = Self;
    fn mul(self, other: ModInt) -> Self {
        self * other.0
    }
}
impl std::ops::Mul<ModInt> for i64 {
    type Output = ModInt;
    fn mul(self, other: ModInt) -> ModInt {
        other * self
    }
}
impl std::ops::MulAssign<i64> for ModInt {
    fn mul_assign(&mut self, other: i64) {
        self.0 = ModInt::new(self.0 * other, self.1).0;
    }
}
impl std::ops::MulAssign for ModInt {
    fn mul_assign(&mut self, other: ModInt) {
        *self *= other.0;
    }
}
impl std::ops::Div for ModInt {
    type Output = Self;
    fn div(self, other: ModInt) -> Self {
        self * other.inv()
    }
}
impl std::ops::Div<i64> for ModInt {
    type Output = Self;
    fn div(self, other: i64) -> Self {
        self / ModInt(other, self.1)
    }
}
impl std::ops::Div<ModInt> for i64 {
    type Output = ModInt;
    fn div(self, other: ModInt) -> ModInt {
        other.inv() * self
    }
}
impl std::ops::DivAssign for ModInt {
    fn div_assign(&mut self, other: ModInt) {
        self.0 = (self.clone() / other).0;
    }
}
impl std::ops::DivAssign<i64> for ModInt {
    fn div_assign(&mut self, other: i64) {
        *self /= ModInt(other, self.1);
    }
}

fn binom(n: ModInt, k: ModInt) -> ModInt {
    if k.0 == 0 {
        ModInt(1, n.1)
    } else if n.0 < k.0 * 2 {
        binom(n, n - k)
    } else {
        let mut c = ModInt(1, n.1);
        for i in 0..k.0 {
            c *= n - i;
            c /= k - i;
        }
        c
    }
}

/// x = binom(n, k) => binom(n, k+1)
fn binom_increment(x: ModInt, n: i64, k: i64) -> ModInt {
    x * (n - k) / (k + 1)
}

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.cin();
    let s: String = sc.cin();
    let m = s.len();

    let mut ac = ModInt(1, M);
    let mut ans = ModInt(0, M);
    for i in 0..n + 1 {
        ans += ac * ModInt(25, M).pow(i as i64);
        ac = binom_increment(ac, (m + n) as i64, i as i64);
    }
    put!(ans);
}

use std::collections::VecDeque;
use std::io::{self, Write};
use std::str::FromStr;

struct Scanner {
    stdin: io::Stdin,
    buffer: VecDeque<String>,
}
impl Scanner {
    fn new() -> Self {
        Scanner {
            stdin: io::stdin(),
            buffer: VecDeque::new(),
        }
    }
    fn cin<T: FromStr>(&mut self) -> T {
        while self.buffer.is_empty() {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
        self.buffer.pop_front().unwrap().parse::<T>().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> {
        self.cin::<String>().chars().collect()
    }
    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.cin()).collect()
    }
}