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 (Python):


from collections import Counter

MOD = 10**9 + 7
MAX = 2000001
def solve():
    k = int(input())
    s = input().strip()
    ns = len(s)
    res = 0
    fac = [1,1] + [0] * MAX
    inv = [1,1] + [0] * MAX
    for i in range(2,MAX+1):
        fac[i] = fac[i-1] * i % MOD
    inv[MAX] = pow(fac[MAX],MOD-2,MOD)
    for i in range(MAX-1,1,-1):
        inv[i] = inv[i+1]*(i+1)%MOD

    def c(a,b):
        return fac[b]*inv[a]*inv[b-a] % MOD



    for left in range(0,k+1):
        right = k - left
        temp = pow(25,left,MOD) * pow(26,right,MOD)
        temp *= c(ns - 1, left + ns -1)
        temp %= MOD
        res += temp
        res %= MOD
    print(res)







if __name__ == '__main__':
    solve()

Solution (Python):
def main(sample_file = ''):

    """ convenient functions
    
    
    
    
    
    """

    """convenient decorator
    
    
        
        
        
        
        
        
        
        
        
        
    """
    
    
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product, combinations_with_replacement 
    
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  
        b, e = 2, 0  
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):   
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict 
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest 
    from copy import deepcopy, copy 
    import operator
    from operator import itemgetter 
    
    
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd
    def gcd(a,b):
        
        
        if a<b:
            a, b = b, a
        while a%b !=0 :
            a, b = b, a%b
        return b

    
    
    
    
    
    

    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)

    
    def sieve_of_eratosthenes(end, typecode="L"):
        
        

        
        import array
        import textwrap
        assert end > 1
        
        
        
        is_prime = array.array("B", (True for i in range(end)))
        
        is_prime[0] = False
        is_prime[1] = False
        
        primes = array.array(typecode)
        
        for i in range(2, end):
            if is_prime[i]:
                primes.append(i)
                for j in range(2 * i, end, i):
                    is_prime[j] = False  
        return primes

    class PrimeFactorization:
        '''初期化にO(NloglogN)/ 因数分解クエリをO(log(k))/ 素数判定クエリをO(1)
        >>> pf = PrimeFactorization(100)
        >>> pf.query(100)
        ((2, 2), (5, 2))
        
        '''
        
        
        
        
        
        
        
        def __init__(self, Num=10**6):
            from collections import defaultdict
            from math import floor
            self.Num = Num
            self.D = [-1] * (Num+1)
            for i in range(2, Num+1):
                if self.D[i] != -1:
                    continue
                self.D[i] = i
                for j in range(1, floor(Num/i)+1):
                    if self.D[j*i] != -1:
                        continue
                    else:
                        self.D[j*i] = i
        
        def query(self, k):
            ans = defaultdict(int)
            tmp = k
            while self.D[tmp] != -1:
                div = self.D[tmp]
                ans[div] += 1
                tmp = tmp//div
            return tuple(ans.items())
        
        def is_prime(self, k):
            return k == self.D[k]

    
    
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    AtoZ = list('abcdefghijklmnopqrstuvwxyz') 
    modpow = lambda a, n, p = MOD: pow(a, n, p) 
    def modinv(a, p = MOD):
        
        
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        
        
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something like:
        >>      pass
        >>  else:
        >>      do something like:
        >>      L[find_root(a)] = L[find_root(a)] + L[find_root(b)]
        >>      L[find_root(b)] = L[find_root(a)]
        >>      
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    
    
    
    class SegTree:
        """
        ref: https://qiita.com/takayg1/items/c811bd07c21923d7ec69
        init(init_val, ide_ele): 配列init_valで初期化 O(N)
        update(k, x): k番目の値をxに更新 O(logN)
        query(l, r): 区間[l, r)をsegfuncしたものを返す O(logN)
        
        ex: seg = SegTree([14, 5, 9, 13], min, float('inf'))
        """
        def __init__(self, init_val, segfunc, ide_ele):
            """
            init_val: 配列の初期値
            segfunc: 区間にしたい操作
            ide_ele: 単位元
            n: 要素数
            num: n以上の最小の2のべき乗
            tree: セグメント木(1-index)
            """
            n = len(init_val)
            self.segfunc = segfunc
            self.ide_ele = ide_ele
            self.num = 1 << (n - 1).bit_length()
            self.tree = [ide_ele] * 2 * self.num
            
            for i in range(n):
                self.tree[self.num + i] = init_val[i]
            
            for i in range(self.num - 1, 0, -1):
                self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])

        def update(self, k, x):
            """
            k番目の値をxに更新
            k: index(0-index)
            x: update value
            """
            k += self.num
            self.tree[k] = x
            while k > 1:
                self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1])
                k >>= 1

        def query(self, l, r):
            """
            [l, r)のsegfuncしたものを得る
            l: index(0-index)
            r: index(0-index)
            """
            res = self.ide_ele
            l += self.num
            r += self.num
            while l < r:
                if l & 1:
                    res = self.segfunc(res, self.tree[l])
                    l += 1
                if r & 1:
                    res = self.segfunc(res, self.tree[r - 1])
                l >>= 1
                r >>= 1
            return res

    
    
    
    
    
    
    
    

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    
    def warshall_floyd(number_vertex, XYD, shift_one_for_vertex=False):
        
        
        
        
        
        d = [[float("inf")]*number_vertex for i in range(number_vertex)]
        for x, y, dist in XYD:
            if shift_one_for_vertex:
                x = x - 1
                y = y - 1
            d[x][y] = dist
            d[y][x] = dist
        for i in range(number_vertex):
            d[i][i] = 0 
        for k in range(number_vertex):
            for i in range(number_vertex):
                for j in range(number_vertex):
                    d[i][j] = min(d[i][j],d[i][k] + d[k][j])
        return d


    """ initialize variables and set inputs
    
        
        
            
            
    
        
        
        
        
        
        
        
    
        
        
        
        
    
        
        
    """

    
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    r_float = lambda: float(r())
    R = lambda: list(map(int, r().split()))
    R_str = lambda: r().split()
    R_map = lambda: map(int, r().split())
    R_float = lambda: list(map(float, r().split()))
    R_tuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    
    
    
    
    
    
    
    """

    
    if sample_file:
        sys.stdin = open(sample_file)
        
    
    
    
    K = r_int()
    S = len(r())
    
    ans = 0
    MOD = 10**9+7
    l = [1] * (K+1)
    r = [1] * (K+1)
    m = [1] * (K+1)
    for i in range(1, K+1):
        l[i] = (l[i-1] * 25)%MOD
        r[i] = (r[i-1] * 26)%MOD
        m[i] = (moddiv(m[i-1] * (S-1+i) , (i)))%MOD
    
    for i in range(K+1):
        ans = (ans + m[i]*l[i]*r[K-i])%MOD
    
    print(int(ans))
    
    
    
    

    """memo: how to use defaultdict of list
    
    Dic = defaultdict(list)
    
    Dic[x].append(y)
    
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    
    >>> a = 5
    >>> bin_str_a = format(a, '
    >>> print(bin_str_a)
    0b0101 
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Solution (Python):
def COMinit():
    fac[0] = fac[1] = 1
    finv[0] = finv[1] = 1
    inv[1] = 1
    for i in range(2,max):
        fac[i] = fac[i-1]*i%mod
        inv[i] = mod - inv[mod%i]*(mod//i)%mod
        finv[i] = finv[i-1]*inv[i]%mod

def COM(n,k):
    if n < k:
        return 0
    if n < 0 or k < 0:
        return 0
    return fac[n] * (finv[k]*finv[n-k]%mod)%mod

mod = 10**9+7

K = int(input())
S = input()
N = len(S)
max = N+K
fac = [0] * max
finv = [0] * max
inv = [0] * max
COMinit()

ans = 0
for i in range(K+1):
    x = COM(N+K-i-1,N-1)
    y = pow(26,i,mod)
    z = pow(25,K-i,mod)
    xyz = ((x*y%mod)*z)%mod
    ans = (ans+xyz)%mod
print(ans)

Solution (Python):
def COMinit():
    fac[0] = fac[1] = 1
    finv[0] = finv[1] = 1
    inv[1] = 1
    for i in range(2,max):
        fac[i] = fac[i-1]*i%mod
        inv[i] = mod - inv[mod%i]*(mod//i)%mod
        finv[i] = finv[i-1]*inv[i]%mod

def COM(n,k):
    if n < k:
        return 0
    if n < 0 or k < 0:
        return 0
    return fac[n] * (finv[k]*finv[n-k]%mod)%mod

mod = 10**9+7

K = int(input())
S = input()
N = len(S)
max = N+K
fac = [0] * max
finv = [0] * max
inv = [0] * max
COMinit()
modlist1 = []
modlist2 = []
a = 1
b = 1
for i in range(K+1):
    modlist1.append(a)
    modlist2.append(b)
    a = a*26%mod
    b = b*25%mod

ans = 0
for i in range(K+1):
    x = COM(N+K-i-1,N-1)
    y = modlist1[i]
    z = modlist2[K-i]
    xyz = ((x*y%mod)*z)%mod
    ans = (ans+xyz)%mod
print(ans)

Solution (Python):

k = int(input())
n = len(input())

mod = 10 ** 9 + 7
f = [1] + [1]
for i in range(2, n + k + 1 + 26):
    f.append(f[-1] * i % mod)

inv = [0] + [1]
for i in range(2, n + k + 2 + 26):
    inv += [inv[mod % i] * (mod - int(mod / i)) % mod]

inv_f = [1, 1]
for i in range(2, n + k + 2 + 26):
    inv_f.append(inv_f[-1] * inv[i] % mod)


def c(x, y):
    return f[x] * inv_f[x - y] * inv_f[y]


ans = 0

for i in range(k + 1):
    ans += c(n + k - i - 1, n - 1) * pow(25,k-i,mod)*pow(26,i,mod)

print(ans % mod)

Solution (Python):
K = int(input())
S = input()
L = len(S)

MOD = 10 ** 9 + 7
modinv = lambda a, mod=MOD: pow(a, MOD - 2, mod)


x = pow(26, K, MOD)


comb = 1

ans = 0
for i in range(K, -1, -1):
    ans = (ans + comb * x) % MOD
    x = x * 25 * modinv(26) % MOD
    comb = comb * (L + K - i) * modinv(K - i + 1) % MOD
print(ans)

Solution (Python):
def getN():
    return int(input())
def getNM():
    return map(int, input().split())
def getList():
    return list(map(int, input().split()))
def getArray(intn):
    return [int(input()) for i in range(intn)]
def input():
    return sys.stdin.readline().rstrip()
def rand_N(ran1, ran2):
    return random.randint(ran1, ran2)
def rand_List(ran1, ran2, rantime):
    return [random.randint(ran1, ran2) for i in range(rantime)]
def rand_ints_nodup(ran1, ran2, rantime):
  ns = []
  while len(ns) < rantime:
    n = random.randint(ran1, ran2)
    if not n in ns:
      ns.append(n)
  return sorted(ns)

def rand_query(ran1, ran2, rantime):
  r_query = []
  while len(r_query) < rantime:
    n_q = rand_ints_nodup(ran1, ran2, 2)
    if not n_q in r_query:
      r_query.append(n_q)
  return sorted(r_query)

from collections import defaultdict, deque, Counter
from sys import exit
from decimal import *
from heapq import heapify, heappop, heappush
import math
import random
import string
from copy import deepcopy
from itertools import combinations, permutations, product
from operator import mul, itemgetter
from functools import reduce
from bisect import bisect_left, bisect_right

import sys
sys.setrecursionlimit(1000000000)
mod = 10 ** 9 + 7





"""
dp[i][j]を
「i文字目まででj回Sの文字を使ったか」とする

K = 5
S = 'oof'
dp = [[0] * (len(S) + 1) for i in range(K + len(S) + 1)]
dp[0][0] = 1

for i in range(1, K + len(S) + 1):
    for j in range(len(S) + 1):
        if j < len(S):
            dp[i][j] += dp[i - 1][j] * 25
        else:
            dp[i][j] += dp[i - 1][j] * 26 
        if j >= 1:
            dp[i][j] += dp[i - 1][j - 1]

l_s = len(S)
どのタイミングで「この先ずっと*= 26」になるか
後ろからi文字目にSを使い切る: pow(25, K - k, mod) * cmb(N + K - k - 1, N - 1) * pow(26, k, mod)
...
"""

lim = 2 * (10 ** 6) + 1
fact = [1, 1]
factinv = [1, 1]
inv = [0, 1]

for i in range(2, lim + 1):
    fact.append((fact[-1] * i) % mod)
    inv.append((-inv[mod % i] * (mod // i)) % mod)
    
    factinv.append((factinv[-1] * inv[-1]) % mod)

def cmb(n, r):
    if (r < 0) or (n < r):
        return 0
    if r == 0:
        return 1
    r = min(r, n - r)
    return fact[n] * factinv[r] * factinv[n - r] % mod

K = getN()
S = input()
N = len(S)

ans = 0


for k in range(K + 1):
    
    ans += cmb(N + K - k - 1, N - 1) * pow(26, k, mod) * pow(25, K - k, mod) % mod
    ans %= mod

print(ans)

Solution (Python):
MOD = 10**9 + 7
K = int(input())
S = input()
N = len(S)


class Combination:
    """
  O(n)の前計算を1回行うことで，O(1)でnCr mod mを求められる
  n_max = 10**6のとき前処理は約950ms (PyPyなら約340ms, 10**7で約1800ms)
  使用例：
  comb = Combination(1000000)
  print(comb(5, 3))  
  """

    def __init__(self, n_max, mod=10 ** 9 + 7):
        self.mod = mod
        self.modinv = self.make_modinv_list(n_max)
        self.fac, self.facinv = self.make_factorial_list(n_max)

    def __call__(self, n, r):
        if n < r or n < 0 or r < 0:
            return 0
        return self.fac[n] * self.facinv[r] % self.mod * self.facinv[n - r] % self.mod

    def make_factorial_list(self, n):
        
        
        fac = [1]
        facinv = [1]
        for i in range(1, n + 1):
            fac.append(fac[i - 1] * i % self.mod)
            facinv.append(facinv[i - 1] * self.modinv[i] % self.mod)
        return fac, facinv

    def make_modinv_list(self, n):
        
        modinv = [0] * (n + 1)
        modinv[1] = 1
        for i in range(2, n + 1):
            modinv[i] = self.mod - self.mod // i * \
                modinv[self.mod % i] % self.mod
        return modinv


comb = Combination(2100000)
ans = 0
for i in range(K + 1):

    temp = comb(N + K - i - 1, N - 1)
    temp %= MOD
    temp *= pow(26, i, MOD)
    temp %= MOD
    temp *= pow(25, K - i, MOD)
    temp %= MOD
    ans += temp
    ans %= MOD
print(ans)

Solution (Python):
MOD = 10**9 + 7
MAX = 5*10**6 + 1

fact = [0 for _ in range(MAX)]
factinv = [0 for _ in range(MAX)]

fact[0] = 1
for k in range(1, MAX):
    fact[k] = fact[k - 1]*k
    fact[k] %= MOD

factinv[MAX - 1] = pow(fact[MAX - 1], MOD - 2, MOD)
for k in range(MAX - 1, 0, -1):
    factinv[k - 1] = factinv[k]*k
    factinv[k - 1] %= MOD

def nCk(n, k):
    return fact[n]*factinv[k]*factinv[n - k] % MOD

def nPk(n, k):
    return fact[n]*factinv[n - k] % MOD

K = int(input())
S = input()
N = len(S)

ans = 0
for k in range(K + 1):
    ans += nCk(N + K - k - 1, N - 1)*pow(26, k, MOD)*pow(25, K - k, MOD) % MOD
    ans %= MOD

print(ans)

Solution (Python):

k=int(input())
n=len(input())

mod=10**9+7
f=[1]+[1]
for i in range(2,n+k+1+26):
    f.append(f[-1]*i%mod)


inv = [0]+[1]
for i in range(2,n+k+2+26):
  inv += [inv[mod % i] * (mod - int(mod / i)) % mod]
 
inv_f=[1,1]
for i in range(2,n+k+2+26):
    inv_f.append(inv_f[-1]*inv[i]%mod)

def c(x,y):
    return f[x]*inv_f[x-y]*inv_f[y]
ans=0
prod=pow(25,k,mod)
for i in range(k+1):
    ans+=c(n+k-i-1,n-1)*prod
    prod*=26
    prod*=inv[25]
    prod%=mod
print(ans%mod)

Solution (Python):
ma = lambda :map(int,input().split())
lma = lambda :list(map(int,input().split()))
tma = lambda :tuple(map(int,input().split()))
ni = lambda:int(input())
yn = lambda fl:print("Yes") if fl else print("No")
import collections
import math
import itertools
import heapq as hq
nmax = 2*10**6+2
mod = 10**9+7
fac = [1]*nmax
finv = [1]*nmax
inv = [1]*nmax
def ncr_pre():
    for i in range(2,nmax):
        fac[i] = fac[i-1]*i % mod
        inv[i] = mod - inv[mod%i] * (mod//i) %mod
        finv[i] = finv[i-1] * inv[i] %mod

def ncr(n,r):
    if n<r:
        return 0
    if n<0 or r<0:
        return 0
    return fac[n]* (finv[r] * finv[n-r] %mod) %mod

ncr_pre()
k = ni()
s = input()
n = len(s)
ans= 0
for i in range(k+1):
    ans=(ans+ ncr(n+k-i-1,n-1)*pow(25,k-i,mod)*pow(26,i,mod) )%mod
print(ans)

Solution (Python):
P = 10**9+7

fact = [1 for _ in range(2000001)]
inv = [1 for _ in range(2000001)]
fact_inv = [1 for _ in range(2000001)]

for i in range(2, 2000001):
    fact[i] = (fact[i-1]*i) % P
    inv[i] = P - (inv[P % i] * (P // i)) % P
    fact_inv[i] = (fact_inv[i-1] * inv[i]) % P

K = int(input())
S = input()
N = K + len(S)
p = 1
ans = 0
for i in range(K+1):
    ans += p * (fact[N] * fact_inv[N-i] * fact_inv[i] % P)
    ans = ans % P
    p *= 25
    p = p % P

print(ans)

Solution (Python):
MOD = 10 ** 9 + 7

fact = [1, 1]
factinv = [1, 1]
inv = [0, 1]

def init(n):
    for i in range(2, n + 1):
        fact.append((fact[-1] * i) % MOD)
        inv.append((-inv[MOD % i] * (MOD // i)) % MOD)
        factinv.append((factinv[-1] * inv[-1]) % MOD)

def nPk(n, k):
    return fact[n] * factinv[n - k] % MOD

def nCk(n, k):
    return fact[n] * factinv[n - k] * factinv[k] % MOD

K = int(input())
N = len(input())

init(N + K)
p25 = [1]
p26 = [1]

for k in range(K):
    p25.append(p25[-1] * 25 % MOD)
    p26.append(p26[-1] * 26 % MOD)

ans = 0
for m in range(K + 1):
    n = N + K
    ans += p25[K - m] * p26[m] * nCk(n - 1 - m, N - 1) % MOD
print(ans % MOD)

Solution (Python):
import time

MOD = 10 ** 9 + 7

K = int(input())
S = input()
l = len(S)

fac = [1] * (K + l + 1)
invfac = [1] * (K + l + 1)
for i in range(1, K + l + 1):
	fac[i] = (fac[i - 1] * i) % MOD
	invfac[i] = pow(fac[i], MOD - 2, MOD)

p25 = [1] * (K + 1)
p26 = [1] * (K + 1)
for i in range(1, K + 1):
	p25[i] = (p25[i - 1] * 25) % MOD
	p26[i] = (p26[i - 1] * 26) % MOD

ans = 0
for en in range(l - 1, l + K):
	t = (fac[en] * invfac[en - l + 1]) % MOD
	t = (t * invfac[l - 1]) % MOD
	t = (t * p25[en - l + 1]) % MOD
	t = (t * p26[l + K - 1 - en]) % MOD
	ans = (ans + t) % MOD
print(ans)

Solution (Python):
MOD = 10 ** 9 + 7

K = int(input())
S = input()
l = len(S)

fac = [1] * (K + l + 1)
for i in range(1, K + l + 1):
	fac[i] = (fac[i - 1] * i) % MOD

p25 = [1] * (K + 1)
p26 = [1] * (K + 1)
for i in range(1, K + 1):
	p25[i] = (p25[i - 1] * 25) % MOD
	p26[i] = (p26[i - 1] * 26) % MOD

ans = 0
for en in range(l - 1, l + K):
	t = (fac[en] * pow(fac[en - l + 1], MOD - 2, MOD) * pow(fac[l - 1], MOD - 2, MOD)) % MOD
	t = (t * p25[en - l + 1]) % MOD
	t = (t * p26[l + K - 1 - en]) % MOD
	ans = (ans + t) % MOD
print(ans)

Solution (Python):
k = int(input())
s = input()
n = len(s)
mod = 10 ** 9 + 7

fac = [1] * (n + k + 2)
for i in range(1, n + k + 1):
    fac[i] = fac[i - 1] * i % mod


def c(n, k):
    return fac[n] * pow(fac[n - k] * fac[k] % mod, mod - 2, mod) % mod


ans = 0
for i in range(k + 1):
    ans += c(n - 1 + k - i, k - i) * \
        pow(25, k - i, mod) * pow(26, i, mod) % mod
    ans %= mod
print(ans)

Solution (Python):
class Combination:
    """
    SIZEが10^6程度以下の二項係数を何回も呼び出したいときに使う
    使い方:
    comb = Combination(SIZE, MOD)
    comb(10, 3) => 120
    """

    def __init__(self, N, MOD=10 ** 9 + 7):
        self.MOD = MOD
        self.fact, self.inv = self._make_factorial_list(N)

    def __call__(self, n, k):
        if k < 0 or k > n:
            return 0
        res = self.fact[n] * self.inv[k] % self.MOD
        res = res * self.inv[n - k] % self.MOD
        return res

    def _make_factorial_list(self, N):
        fact = [1] * (N + 1)
        inv = [1] * (N + 1)
        MOD = self.MOD
        for i in range(1, N + 1):
            fact[i] = (fact[i - 1] * i) % MOD
        inv[N] = pow(fact[N], MOD - 2, MOD)
        for i in range(N, 0, -1):
            inv[i - 1] = (inv[i] * i) % MOD
        return fact, inv


K = int(input())
S = input()
N = len(S)

mod = 10 ** 9 + 7
comb = Combination(3 * 10 ** 6, mod)

ans = 0
for i in range(K + 1):
    cnt = 1
    L = pow(25, i, mod)
    L *= comb(i + N - 1, i)
    L %= mod
    R = pow(26, K-i, mod)
    ans += L * R % mod
    ans %= mod

print(ans)

Solution (Python):
import sys,queue,math,copy,itertools,bisect,collections,heapq

def main():
    MOD = 10**9 + 7
    NI = lambda : int(sys.stdin.readline())
    SI = lambda : sys.stdin.readline().rstrip()

    K = NI()
    S = SI()
    LS = len(S)

    f = [0] * (K+LS)
    r = [0] * (K+LS)
    f[0] = 1
    r[0] = 1
    c = 1
    for i in range(1, K + LS):
        c = (c * i) % MOD
        f[i] = c
        r[i] = pow(c, MOD - 2, MOD)

    def comb(n, k):
        return (f[n] * r[k] * r[n - k]) % MOD

    ans = 0
    for i in range(K+1):
        ans = (ans + pow(25,i,MOD) * pow(26,K-i,MOD) * comb(i+LS-1,LS-1)) % MOD
    print(ans)

if __name__ == '__main__':
    main()