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



Sample input:
5
oof


Sample output:
575111451

Submission status: Runtime Error

Solution code:
 
# from math import factorial as fac
from collections import defaultdict
# from copy import deepcopy
import sys, math
f = None
try:
	f = open('q1.input', 'r')
except IOError:
	f = sys.stdin
if 'xrange' in dir(__builtins__):
	range = xrange
# print(f.readline())
sys.setrecursionlimit(10**2)

	
def print_case_iterable(case_num, iterable):
	print("Case #{}: {}".format(case_num," ".join(map(str,iterable))))

def print_case_number(case_num, iterable):
	print("Case #{}: {}".format(case_num,iterable))

def print_iterable(A):
	print (' '.join(A))

def read_int():
	return int(f.readline().strip())
def read_int_array():
	return [int(x) for x in f.readline().strip().split(" ")]
def rns():
	a =  [x for x in f.readline().split(" ")]
	return int(a[0]), a[1].strip()
def read_string():
	return list(f.readline().strip())
def ri():
	return int(f.readline().strip())
def ria():
	return [int(x) for x in f.readline().strip().split(" ")]
def rns():
	a =  [x for x in f.readline().split(" ")]
	return int(a[0]), a[1].strip()
def rs():
	return list(f.readline().strip())
def bi(x):
	return bin(x)[2:]





from collections import deque
import math
NUMBER = 10**9 + 7
# NUMBER = 998244353
def factorial(n) : 
	M = NUMBER
	f = 1
  
	for i in range(1, n + 1):  
		f = (f * i) % M # Now f never can  
						# exceed 10^9+7  
	return f
def mult(a,b):
	return (a * b) % NUMBER

def minus(a , b):
	return (a - b) % NUMBER

def plus(a , b):
	return (a + b) % NUMBER

def egcd(a, b):
	if a == 0:
		return (b, 0, 1)
	else:
		g, y, x = egcd(b % a, a)
		return (g, x - (b // a) * y, y)

def modinv(a):
	m = NUMBER
	g, x, y = egcd(a, m)
	if g != 1:
		raise Exception('modular inverse does not exist')
	else:
		return x % m
def choose(n,k):
	if n < k:
		assert false
	return  mult(factorial(n), modinv(mult(factorial(k),factorial(n-k)))) % NUMBER
from collections import deque, defaultdict 
import heapq


from types import GeneratorType
def bootstrap(f, stack=[]):
	def wrappedfunc(*args, **kwargs):
		if stack:
			return f(*args, **kwargs)
		else:
			to = f(*args, **kwargs)
			while True:
				if type(to) is GeneratorType:
					stack.append(to)
					to = next(to)
				else:
					stack.pop()
					if not stack:
						break
					to = stack[-1].send(to)
			return to

	return wrappedfunc


def dfs(g, timeIn, timeOut,depths,parents): 
	# assign In-time to node u 
	cnt = 0
	# node, neig_i, parent, depth
	stack = [[1,0,0,0]]
	while stack:
		v,neig_i,parent,depth = stack[-1]
		parents[v] = parent
		depths[v] = depth
		# print (v)
		if neig_i == 0:
			timeIn[v] = cnt    
			cnt+=1
		while neig_i < len(g[v]):
			u = g[v][neig_i]
			if u == parent:
				neig_i+=1
				continue
			stack[-1][1] = neig_i + 1
			stack.append([u,0,v,depth+1])
			break
		if neig_i == len(g[v]):
			stack.pop()
			timeOut[v] = cnt
			cnt += 1
  
def isAncestor(u: int, v: int, timeIn: list, timeOut: list) -> str: 
	return timeIn[u] <= timeIn[v] and timeOut[v] <= timeOut[u] 

cnt = 0
@bootstrap
def dfs(v,adj,timeIn, timeOut,depths,parents,parent=0,depth=0):
	global cnt
	parents[v] = parent
	depths[v] = depth
	timeIn[v] = cnt
	cnt+=1
	for u in adj[v]:
		if u == parent:
			continue
		yield dfs(u,adj,timeIn,timeOut,depths,parents,v,depth+1)
	timeOut[v] = cnt
	cnt+=1
	yield 


def solution(s,n):
	fact = [1]*(10**6+1)
	for i in range(1,10**6+1):
		fact[i] = (fact[i-1]*i)%NUMBER
	def choose(l,r):
		return mult(fact[l],pow(mult(fact[r],fact[l-r]),NUMBER-2,NUMBER))
	summ = 0
	k = len(s)
	n = n+k
	d = 26
	for j in range(n-k+1):
		summ=plus(summ,mult(choose(n,j+k),pow(d-1,n-k-j)))
		# summ=mult(summ,)
	return summ
	
def main():
	T = 1
	# T = ri()
	for i in range(T):
		n = ri()
		s = rs()
		# a = ria()
		# n,k = ria()
		# a=ria()

		x = solution(s,n)
		if 'xrange' not in dir(__builtins__):
			print(x)
		else:
			print >>output,str(x)# "Case #"+str(i+1)+':',
	if 'xrange' in dir(__builtins__):
		print(output.getvalue())
		output.close()

if 'xrange' in dir(__builtins__):
	import cStringIO
	output = cStringIO.StringIO()
#example usage:
#    for l in res:
#       print >>output, str(len(l)) + ' ' +  ' '.join(l)

if __name__ == '__main__':
	main()

Submission status: Runtime Error

Solution code:
 
# from math import factorial as fac
from collections import defaultdict
# from copy import deepcopy
import sys, math
f = None
try:
	f = open('q1.input', 'r')
except IOError:
	f = sys.stdin
if 'xrange' in dir(__builtins__):
	range = xrange
# print(f.readline())
sys.setrecursionlimit(10**2)

	
def print_case_iterable(case_num, iterable):
	print("Case #{}: {}".format(case_num," ".join(map(str,iterable))))

def print_case_number(case_num, iterable):
	print("Case #{}: {}".format(case_num,iterable))

def print_iterable(A):
	print (' '.join(A))

def read_int():
	return int(f.readline().strip())
def read_int_array():
	return [int(x) for x in f.readline().strip().split(" ")]
def rns():
	a =  [x for x in f.readline().split(" ")]
	return int(a[0]), a[1].strip()
def read_string():
	return list(f.readline().strip())
def ri():
	return int(f.readline().strip())
def ria():
	return [int(x) for x in f.readline().strip().split(" ")]
def rns():
	a =  [x for x in f.readline().split(" ")]
	return int(a[0]), a[1].strip()
def rs():
	return list(f.readline().strip())
def bi(x):
	return bin(x)[2:]





from collections import deque
import math
NUMBER = 10**9 + 7
# NUMBER = 998244353
def factorial(n) : 
	M = NUMBER
	f = 1
  
	for i in range(1, n + 1):  
		f = (f * i) % M # Now f never can  
						# exceed 10^9+7  
	return f
def mult(a,b):
	return (a * b) % NUMBER

def minus(a , b):
	return (a - b) % NUMBER

def plus(a , b):
	return (a + b) % NUMBER

def egcd(a, b):
	if a == 0:
		return (b, 0, 1)
	else:
		g, y, x = egcd(b % a, a)
		return (g, x - (b // a) * y, y)

def modinv(a):
	m = NUMBER
	g, x, y = egcd(a, m)
	if g != 1:
		raise Exception('modular inverse does not exist')
	else:
		return x % m
def choose(n,k):
	if n < k:
		assert false
	return  mult(factorial(n), modinv(mult(factorial(k),factorial(n-k)))) % NUMBER
from collections import deque, defaultdict 
import heapq


from types import GeneratorType
def bootstrap(f, stack=[]):
	def wrappedfunc(*args, **kwargs):
		if stack:
			return f(*args, **kwargs)
		else:
			to = f(*args, **kwargs)
			while True:
				if type(to) is GeneratorType:
					stack.append(to)
					to = next(to)
				else:
					stack.pop()
					if not stack:
						break
					to = stack[-1].send(to)
			return to

	return wrappedfunc


def dfs(g, timeIn, timeOut,depths,parents): 
	# assign In-time to node u 
	cnt = 0
	# node, neig_i, parent, depth
	stack = [[1,0,0,0]]
	while stack:
		v,neig_i,parent,depth = stack[-1]
		parents[v] = parent
		depths[v] = depth
		# print (v)
		if neig_i == 0:
			timeIn[v] = cnt    
			cnt+=1
		while neig_i < len(g[v]):
			u = g[v][neig_i]
			if u == parent:
				neig_i+=1
				continue
			stack[-1][1] = neig_i + 1
			stack.append([u,0,v,depth+1])
			break
		if neig_i == len(g[v]):
			stack.pop()
			timeOut[v] = cnt
			cnt += 1
  
def isAncestor(u: int, v: int, timeIn: list, timeOut: list) -> str: 
	return timeIn[u] <= timeIn[v] and timeOut[v] <= timeOut[u] 

cnt = 0
@bootstrap
def dfs(v,adj,timeIn, timeOut,depths,parents,parent=0,depth=0):
	global cnt
	parents[v] = parent
	depths[v] = depth
	timeIn[v] = cnt
	cnt+=1
	for u in adj[v]:
		if u == parent:
			continue
		yield dfs(u,adj,timeIn,timeOut,depths,parents,v,depth+1)
	timeOut[v] = cnt
	cnt+=1
	yield 


def solution(s,n):
	fact = [1]*(10**6+1)
	for i in range(1,10**6+1):
		fact[i] = (fact[i-1]*i)%NUMBER
	def choose(l,r):
		return mult(fact[l],modinv(mult(fact[r],fact[l-r])))
	summ = 0
	k = len(s)
	n = n+k
	d = 26
	for j in range(n-k+1):
		summ=plus(summ,mult(choose(n,j+k),pow(d-1,n-k-j)))
		# summ=mult(summ,)
	return summ
	
def main():
	T = 1
	# T = ri()
	for i in range(T):
		n = ri()
		s = rs()
		# a = ria()
		# n,k = ria()
		# a=ria()

		x = solution(s,n)
		if 'xrange' not in dir(__builtins__):
			print(x)
		else:
			print >>output,str(x)# "Case #"+str(i+1)+':',
	if 'xrange' in dir(__builtins__):
		print(output.getvalue())
		output.close()

if 'xrange' in dir(__builtins__):
	import cStringIO
	output = cStringIO.StringIO()
#example usage:
#    for l in res:
#       print >>output, str(len(l)) + ' ' +  ' '.join(l)

if __name__ == '__main__':
	main()

Submission status: Runtime Error

Solution code:
import sys

sys.setrecursionlimit(10 ** 7)
rl = sys.stdin.readline


class Combination:
    def __init__(self, n: int, mod: int):
        self.mod = mod
        self.fact = [0] * (n + 1)
        self.factinv = [0] * (n + 1)
        self.inv = [0] * (n + 1)
        
        self.fact[0] = self.fact[1] = 1
        self.factinv[0] = self.factinv[1] = 1
        self.inv[1] = 1
        for i in range(2, n + 1):
            self.fact[i] = (self.fact[i - 1] * i) % mod
            self.inv[i] = (-self.inv[mod % i] * (mod // i)) % mod
            self.factinv[i] = (self.factinv[i - 1] * self.inv[i]) % mod
    
    def ncr(self, n: int, r: int):
        if r < 0 or n < r:
            return 0
        r = min(r, n - r)
        return self.fact[n] * self.factinv[r] % self.mod * self.factinv[n - r] % self.mod
    
    def nhr(self, n: int, r: int):
        return self.ncr(n + r - 1, r)
    
    def npr(self, n: int, r: int):
        if r < 0 or n < r:
            return 0
        return self.fact[n] * self.factinv[n - r] % self.mod


def solve():
    K = int(rl())
    S = rl().rstrip()
    MOD = 10 ** 9 + 7
    
    com = Combination(2 * 10 ** 5 + 10, MOD)
    n = len(S)
    m = n + K
    ans = 0
    for i in range(n, m + 1):
        j = m - i
        ans += com.ncr(n + K - j - 1, n - 1) * pow(25, K - j, MOD) * pow(26, j, MOD)
        ans %= MOD
    print(ans)


if __name__ == '__main__':
    solve()

Submission status: Runtime Error

Solution code:
def main():
    k = int(input())
    s = input()
    n = len(s)

    def cmb1(n, r, mod):
        if ( r<0 or r>n ):
            return 0
        r = min(r, n-r)
        return g1[n] * g2[r] * g2[n-r] % mod

    mod = 10**9+7 #出力の制限
    N = 10**6
    g1 = [1, 1] # 元テーブル
    g2 = [1, 1] #逆元テーブル
    inverse = [0, 1] #逆元テーブル計算用テーブル

    for i in range( 2, N + 1 ):
        g1.append( ( g1[-1] * i ) % mod )
        inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
        g2.append( (g2[-1] * inverse[-1]) % mod )

    def power(a, n, mod):
        bi=str(format(n,"b")) #2進数
        res=1
        for i in range(len(bi)):
            res=(res*res) %mod
            if bi[i]=="1":
                res=(res*a) %mod
        return res

    ans = 0
    for i in range(k+1):
        temp = power(25, i, mod)
        temp *= cmb1(i+n-1, n-1, mod)
        temp %= mod
        temp *= power(26, k-i, mod)
        temp %= mod
        ans += temp
    print(ans%mod)

if __name__ == '__main__':
    main()

Submission status: Runtime Error

Solution code:
k = int(input())
# s = input()
# s = len(s)
s = int(input())

mod = 10 ** 9 + 7
n = k + s


def _fac_inv(_n, _mod):
    _fac = [1] * (_n + 1)
    _inv = [1] * (_n + 1)
    for i in range(_n):
        _fac[i + 1] = _fac[i] * (i + 1) % _mod
    _inv[_n] = pow(_fac[_n], _mod - 2, _mod)
    for i in range(_n, 0, -1):
        _inv[i - 1] = _inv[i] * i % _mod

    return _fac, _inv


fac, inv = _fac_inv(n, mod)

n25 = [1]
n26 = [1]
for _ in range(n-s):
    n25.append((n25[-1] * 25) % mod)
    n26.append((n26[-1] * 26) % mod)

ans = 0

for i in range(s, n + 1):
    ans = (ans + fac[i-1] * inv[s-1] * inv[i-s] * n25[i-s] * n26[n-i]) % mod

print(ans)

Submission status: Runtime Error

Solution code:
https://kkt89.hatenablog.com/entry/2020/06/21/ABC171_F-Strivore

Submission status: Runtime Error

Solution code:
k = int(input())
s = input()

mod = 10**9+7

def fpow(x, y):
  res = 1
  while y>0:
    if y%2:
      res = (res%mod * x%mod)%mod
    x = (x%mod * x%mod)%mod
    y = y//2
  return res
MAXN = 10**6+5
fact = [0]*MAXN
fact[0] = 1
for i in range(1, MAXN):
  fact[i] = (i%mod * fact[i-1]%mod)%mod
  
def inv(a):
  return fpow(a, mod-2)
  
n = len(s)
ans = fpow(26, n+k)
for m in range(n):
    ncm = (fact[n+k]%mod * inv(fact[m])%mod)%mod
    ncm = (ncm%mod * inv(fact[n+k-m])%mod)%mod
    
    p = fpow(25, n+k-m)
    
    val = (ncm%mod * p%mod)%mod
    
    ans = (ans%mod - val%mod + mod)%mod
print(ans%mod)

Submission status: Runtime Error

Solution code:
import sys
readline = sys.stdin.readline
MOD = 10**9+7
def frac(limit):
    frac = [1]*limit
    for i in range(2,limit):
        frac[i] = i * frac[i-1]%MOD
    fraci = [None]*limit
    fraci[-1] = pow(frac[-1], MOD -2, MOD)
    for i in range(-2, -limit-1, -1):
        fraci[i] = fraci[i+1] * (limit + i + 1) % MOD
    return frac, fraci

frac, fraci = frac(1341398)
def cmb(a, b):
    if not a >= b >= 0:
        return 0
    return frac[a]*fraci[b]*fraci[a-b]%MOD

K, = map(int, input().split())
t = len(input().strip())

R = 0
for x in range(K+1):
    R += cmb(K+t-x-1, t-1)*pow(25, K-x, MOD)*pow(26, x, MOD)%MOD
    R %= MOD
print(R)

Submission status: Runtime Error

Solution code:
MOD = 10**9 + 7
m = 10**6 + 5
fac = [0] * m
finv = [0] * m
inv = [0] * m


def COMBinitialize(m):
    fac[0] = 1
    finv[0] = 1
    if m > 1:
        fac[1] = 1
        finv[1] = 1
        inv[1] = 1
        for i in range(2, m):
            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 COMB(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


def main():
    K = int(input())
    S = input()
    N = len(S)
    ans = 0
    COMBinitialize(m)
    for i in range(K+1):
        ans += COMB(N-1+K-i, N-1) * pow(25, (K-i), MOD) * pow(26, i, MOD)
        ans %= MOD
    print(ans)


if __name__ == '__main__':
    main()

Submission status: Runtime Error

Solution code:
k=int(input())
s=input()

U=10**6+1
mod=10**9+7

fact=[1]*(U+1)
fact_inv=[1]*(U+1)

for i in range(1,U+1):
    fact[i]=(fact[i-1]*i)%mod
fact_inv[U]=pow(fact[U],mod-2,mod)

for i in range(U,0,-1):
	fact_inv[i-1]=(fact_inv[i]*i)%mod

def comb(n,k):
    if k<0 or k>n:
        return 0
    x=fact[n]
    x*=fact_inv[k]
    x%=mod
    x*=fact_inv[n-k]
    x%=mod
    return x
m=len(s)
ans=0
for i in range(k+1):
    ans=(ans+pow(25,i,mod)*comb(m+i-1,m-1)*pow(26,k-i,mod))%mod
print(ans)

Submission status: Runtime Error

Solution code:
k=int(input())
s=input()

U=2*10**5
mod=10**9+7

fact=[1]*(U+1)
fact_inv=[1]*(U+1)

for i in range(1,U+1):
    fact[i]=(fact[i-1]*i)%mod
fact_inv[U]=pow(fact[U],mod-2,mod)

for i in range(U,0,-1):
	fact_inv[i-1]=(fact_inv[i]*i)%mod

def comb(n,k):
    if k<0 or k>n:
        return 0
    x=fact[n]
    x*=fact_inv[k]
    x%=mod
    x*=fact_inv[n-k]
    x%=mod
    return x
m=len(s)
ans=0
for i in range(k+1):
    ans=(ans+pow(25,i,mod)*comb(m+i-1,m-1)*pow(26,k-i,mod))%mod
print(ans)

Submission status: Runtime Error

Solution code:
k=int(input())
s=input()
ans=0
mod=1000000007
x=220000
fact=[0]*x
invfact=[0]*x
fact[0]=1
for i in range(1,x):
    fact[i]=fact[i-1]*i%mod
invfact[x-1]=pow(fact[x-1],mod-2,mod)
for i in range(x-2,-1,-1):
    invfact[i]=invfact[i+1]*(i+1)%mod
def nCk(n,k):
    return(fact[n]*invfact[k]*invfact[n-k])%mod
for i in range(0,k+1):
    # print(nCk(len(s)+i-1,i),pow(25,i,mod),pow(26,k-i,mod))
    ans+=nCk(len(s)+i-1,i)*pow(25,i,mod)*pow(26,k-i,mod)
print(ans%mod)

Submission status: Runtime Error

Solution code:
K = int(input())
S = input()
SS = len(S)

nCr = {}
def cmb(n, r):
    if r == 0 or r == n: return 1
    if r == 1: return n
    if (n,r) in nCr: return nCr[(n,r)]
    nCr[(n,r)] = cmb(n-1,r) + cmb(n-1,r-1)
    return nCr[(n,r)]

ans = 0
for i in range(K + 1):
	a = 25 ** i * cmb(i + SS - 1,  SS - 1) * 26 ** (K - i)
	ans += a
print(ans % (10 ** 9 + 7))

Submission status: Runtime Error

Solution code:
MAXN = 10**6+1
p = 10**9 + 7

fact = [1] * MAXN
invfact = [1] * MAXN
for i in range(1, MAXN):
    fact[i] = fact[i-1] * i % p
invfact[MAXN-1] = pow(fact[MAXN-1], p-2, p)
for i in range(MAXN-1, 0, -1):
    invfact[i-1] = invfact[i] * i % p
    
def nCk(n, k):
    return fact[n] * invfact[n-k] * invfact[k] % p

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

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

Submission status: Runtime Error

Solution code:
k = int(input())
s = input()
n = len(s)
MOD = 10**9+7
ans = 0

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

N = 10 ** 6
fact = [1, 1]
factinv = [1, 1]
inv = [0, 1]
 
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)

for i in range(k+1):
    b = pow(26, k-i, MOD)
    b *= pow(25, i, MOD)
    b *= cmb(i+n-1, n-1, MOD)
    ans += (b % MOD)
    
print(ans%MOD)

Submission status: Runtime Error

Solution code:
K = int(input())
S = input()
MOD = 10**9 + 7

length = len(S)
length_all = K + length
ans = 0
list_25 = [1] * (10**6 + 5)
list_26 = [1] * (10**6 + 5)
for i in range(1,10**6 + 5):
  list_25[i] = list_25[i - 1] * 25 % MOD
  list_26[i] = list_26[i - 1] * 26 % MOD
  
fact = [1] * (10**6 + 5)
fact_inv = [1] * (10**6 + 5)
inv = [1] * (10**6 + 5)
for i in range(1, 10**6 + 5):
  fact[i] = fact[i-1] * i % MOD
  fact_inv[i] = fact_inv[i - 1] * pow(i, MOD - 2, MOD) % MOD
for i in range(K + 1):
  ans += list_26[i] * list_25[K - i] % MOD * fact[length_all - i - 1] * fact_inv[length - 1] * fact_inv[K - i] % MOD

print(ans % MOD)

Submission status: Runtime Error

Solution code:
import sys
import math
import collections

sys.setrecursionlimit(10 ** 8)

input = sys.stdin.readline


def main():
    K = int(input())
    S = input().strip()

    MOD = 10 ** 9 + 7

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

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

    N = 10 ** 6 + 5000
    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)

    ans = 0
    for i in range(K + 1):
        if len(S) == 1:
            ans += pow(25, i, MOD) * pow(26, K - i, MOD)
        else:
            ans += pow(25, i, MOD) * cmb(i + len(S) - 1, len(S) - 1, MOD) * pow(26, K - i, MOD)

    print(ans % MOD)


if __name__ == '__main__':
    main()

Submission status: Runtime Error

Solution code:
# coding: utf-8
import sys
import numpy as np

sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

MOD = 10 ** 9 + 7

def perm(n,k):
    if k > n or k < 0: return 0
    return fact[n] * fact_inv[n-k] % MOD

def cmb(n, k):
    if k < 0 or k > n: return 0
    return fact[n] * fact_inv[k] % MOD * fact_inv[n-k] % MOD

def cumprod(arr, MOD):
    L = len(arr); Lsq = int(L**.5+1)
    arr = np.resize(arr, Lsq**2).reshape(Lsq, Lsq)
    for n in range(1, Lsq):
        arr[:, n] *= arr[:, n-1]; arr[:, n] %= MOD
    for n in range(1, Lsq):
        arr[n] *= arr[n-1, -1]; arr[n] %= MOD
    return arr.ravel()[:L]

def make_fact(U, MOD):
    x = np.arange(U, dtype=np.int64); x[0] = 1
    fact = cumprod(x, MOD)
    x = np.arange(U, 0, -1, dtype=np.int64); x[0] = pow(int(fact[-1]), MOD-2, MOD)
    fact_inv = cumprod(x, MOD)[::-1]
    return fact, fact_inv

U = 10 ** 6 + 100 # 階乗テーブルの上限
fact, fact_inv = make_fact(U, MOD)
K = ir()
S = sr()
length = len(S)
# Sの文字の最後の位置
answer = 0
for i in range(length-1, length+K):
    temp = cmb(i, length-1) * pow(25, i + 1 - length, MOD) % MOD
    temp *= pow(26, length+K-i-1, MOD)
    temp %= MOD
    answer += temp

print(answer%MOD)

Submission status: Runtime Error

Solution code:
# coding: utf-8
import sys
import numpy as np

sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

MOD = 10 ** 9 + 7

def perm(n,k):
    if k > n or k < 0: return 0
    return fact[n] * fact_inv[n-k] % MOD

def cmb(n, k):
    if k < 0 or k > n: return 0
    return fact[n] * fact_inv[k] % MOD * fact_inv[n-k] % MOD

def cumprod(arr, MOD):
    L = len(arr); Lsq = int(L**.5+1)
    arr = np.resize(arr, Lsq**2).reshape(Lsq, Lsq)
    for n in range(1, Lsq):
        arr[:, n] *= arr[:, n-1]; arr[:, n] %= MOD
    for n in range(1, Lsq):
        arr[n] *= arr[n-1, -1]; arr[n] %= MOD
    return arr.ravel()[:L]

def make_fact(U, MOD):
    x = np.arange(U, dtype=np.int64); x[0] = 1
    fact = cumprod(x, MOD)
    x = np.arange(U, 0, -1, dtype=np.int64); x[0] = pow(int(fact[-1]), MOD-2, MOD)
    fact_inv = cumprod(x, MOD)[::-1]
    return fact, fact_inv

U = 10 ** 6 + 100 # 階乗テーブルの上限
fact, fact_inv = make_fact(U, MOD)
K = ir()
S = sr()
length = len(S)
# Sの文字の最後の位置
answer = 0
for i in range(length-1, length+K):
    temp = cmb(i, length-1) * pow(25, i + 1 - length, MOD) % MOD
    temp *= pow(26, length+K-i-1, MOD)
    temp %= MOD
    answer += temp
    print(i, temp)

print(answer%MOD)

Submission status: Runtime Error

Solution code:
import sys
sys.setrecursionlimit(10**7)
input=sys.stdin.readline
K=int(input())
S=input()
M=len(S)
N=K+M
mod=10**9+7
ans=pow(26,N,mod)
class Data():
    def __init__(self):
        self.power=1
        self.rev=1     
class Combi():
    def __init__(self,N,mod):
        self.lists=[Data() for _ in range(N+1)]
        self.mod=mod  
        for i in range(2,N+1):
            self.lists[i].power=((self.lists[i-1].power)*i)%self.mod
        self.lists[N].rev=pow(self.lists[N].power,self.mod-2,self.mod)
        for j in range(N,0,-1):
            self.lists[j-1].rev=((self.lists[j].rev)*j)%self.mod

    def combi(self,K,R):
        if K<R:
            return 0
        else:
            return ((self.lists[K].power)*(self.lists[K-R].rev)*(self.lists[R].rev))%self.mod
        
c=Combi(2*10**6,mod)
for i in range(M):
    ans-=c.combi(N,i)*pow(25,N-i,mod)
    ans%=mod
print(ans)

Submission status: Runtime Error

Solution code:
MOD = 10**9+7
class mint:
    def __init__(self, x):
        self.x = x % MOD if isinstance(x, int) else int(x) % MOD
    def __str__(self):
        return str(self.x)
    __repr__ = __str__
    def __iadd__(self, other):
        self.x += other.x if isinstance(other, mint) else other
        self.x -= MOD if self.x >= MOD else 0
        return self
    def __isub__(self, other):
        self.x += MOD-other.x if isinstance(other, mint) else MOD-other
        self.x -= MOD if self.x >= MOD else 0
        return self
    def __imul__(self, other):
        self.x *= other.x if isinstance(other, mint) else other
        self.x %= MOD
        return self
    def __imod__(self, other):
        self.x %= other.x if isinstance(other, mint) else other
        self.x %= MOD
        return self
    def __add__(self, other):
        return (
            mint(self.x + other.x) if isinstance(other, mint) else
            mint(self.x + other)
        )
    def __sub__(self, other):
        return (
            mint(self.x - other.x) if isinstance(other, mint) else
            mint(self.x - other)
        )
    def __mul__(self, other):
        return (
            mint(self.x * other.x) if isinstance(other, mint) else
            mint(self.x * other)
        )
    def __mod__(self, other):
        return (
            mint(self.x % other.x) if isinstance(other, mint) else
            mint(self.x % other)
        )
    def __truediv__(self, other):
        return (
            mint(
                self.x * pow(other.x, MOD - 2, MOD)
            ) if isinstance(other, mint) else
            mint(self.x * pow(other, MOD - 2, MOD))
        )
    def __pow__(self, other):
        return (
            mint(pow(self.x, other.x, MOD)) if isinstance(other, mint) else
            mint(pow(self.x, other, MOD))
        )
    __radd__ = __add__
    def __rsub__(self, other):
        return (
            mint(other.x - self.x) if isinstance(other, mint) else
            mint(other - self.x)
        )
    __rmul__ = __mul__
    def __rmod__(self, other):
        return (
            mint(other.x % self.x) if isinstance(other, mint) else
            mint(other % self.x)
        )
    def __rtruediv__(self, other):
        return (
            mint(
                other.x * pow(self.x, MOD - 2, MOD)
            ) if isinstance(other, mint) else
            mint(other * pow(self.x, MOD - 2, MOD))
        )
    def __rpow__(self, other):
        return (
            mint(pow(other.x, self.x, MOD)) if isinstance(other, mint) else
            mint(pow(other, self.x, MOD))
        )
class Comb():
    # class <mint> should be imported
    def __init__(self, n):
        self.n = n
        fact = [0]*(n+1) # 1-indexed
        ifact = [0]*(n+1) # 逆元
        fact[0] = mint(1)
        for i in range(1, n+1):
            fact[i] = fact[i-1]*i
        ifact[-1] = pow(fact[-1], MOD-2)
        for i in range(n, 0, -1):
            ifact[i-1] = ifact[i]*i
        self.fact = fact
        self.ifact = ifact
    def calc(self, n, k):
        if k<0 or k>n:
            return 0
        return self.fact[n]*self.ifact[k]*self.ifact[n-k]
cb= Comb(1000005)

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

ans = mint(0)
for i in range(n-1,n+k):
    ans += cb.calc(i,n-1)*pow(25,i-n+1,MOD)*pow(26,n+k-i-1,MOD)

print(ans)

Submission status: Runtime Error

Solution code:
MOD = 10**9+7
class mint:
    def __init__(self, x):
        self.x = x % MOD if isinstance(x, int) else int(x) % MOD
    def __str__(self):
        return str(self.x)
    __repr__ = __str__
    def __iadd__(self, other):
        self.x += other.x if isinstance(other, mint) else other
        self.x -= MOD if self.x >= MOD else 0
        return self
    def __isub__(self, other):
        self.x += MOD-other.x if isinstance(other, mint) else MOD-other
        self.x -= MOD if self.x >= MOD else 0
        return self
    def __imul__(self, other):
        self.x *= other.x if isinstance(other, mint) else other
        self.x %= MOD
        return self
    def __imod__(self, other):
        self.x %= other.x if isinstance(other, mint) else other
        self.x %= MOD
        return self
    def __add__(self, other):
        return (
            mint(self.x + other.x) if isinstance(other, mint) else
            mint(self.x + other)
        )
    def __sub__(self, other):
        return (
            mint(self.x - other.x) if isinstance(other, mint) else
            mint(self.x - other)
        )
    def __mul__(self, other):
        return (
            mint(self.x * other.x) if isinstance(other, mint) else
            mint(self.x * other)
        )
    def __mod__(self, other):
        return (
            mint(self.x % other.x) if isinstance(other, mint) else
            mint(self.x % other)
        )
    def __truediv__(self, other):
        return (
            mint(
                self.x * pow(other.x, MOD - 2, MOD)
            ) if isinstance(other, mint) else
            mint(self.x * pow(other, MOD - 2, MOD))
        )
    def __pow__(self, other):
        return (
            mint(pow(self.x, other.x, MOD)) if isinstance(other, mint) else
            mint(pow(self.x, other, MOD))
        )
    __radd__ = __add__
    def __rsub__(self, other):
        return (
            mint(other.x - self.x) if isinstance(other, mint) else
            mint(other - self.x)
        )
    __rmul__ = __mul__
    def __rmod__(self, other):
        return (
            mint(other.x % self.x) if isinstance(other, mint) else
            mint(other % self.x)
        )
    def __rtruediv__(self, other):
        return (
            mint(
                other.x * pow(self.x, MOD - 2, MOD)
            ) if isinstance(other, mint) else
            mint(other * pow(self.x, MOD - 2, MOD))
        )
    def __rpow__(self, other):
        return (
            mint(pow(other.x, self.x, MOD)) if isinstance(other, mint) else
            mint(pow(other, self.x, MOD))
        )
class Comb():
    # class <mint> should be imported
    def __init__(self, n):
        self.n = n
        fact = [0]*(n+1) # 1-indexed
        ifact = [0]*(n+1) # 逆元
        fact[0] = mint(1)
        for i in range(1, n+1):
            fact[i] = fact[i-1]*i
        ifact[-1] = pow(fact[-1], MOD-2)
        for i in range(n, 0, -1):
            ifact[i-1] = ifact[i]*i
        self.fact = fact
        self.ifact = ifact
    def calc(self, n, k):
        if k<0 or k>n:
            return 0
        return self.fact[n]*self.ifact[k]*self.ifact[n-k]
cb= Comb(100005)

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

ans = mint(0)
for i in range(n-1,n+k):
    ans += cb.calc(i,n-1)*pow(25,i-n+1,MOD)*pow(26,n+k-i-1,MOD)

print(ans)

Submission status: Runtime Error

Solution code:
k=int(input())
s=input()
n=len(s)
c=1
t=1
ans=0
for i in range(k+1):
  ans+=c*t
  ans%=mod
  c*=(n+k-i)*pow(i+1,mod-2,mod)
  c%=mod
  t*=25
  t%=mod
print(ans)

Submission status: Runtime Error

Solution code:
import sys
import math
import collections

sys.setrecursionlimit(10 ** 8)

input = sys.stdin.readline


def main():
    K = int(input())
    S = input().strip()

    MOD = 10 ** 9 + 7

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

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

    N = 10 ** 6
    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)

    ans = 0
    for i in range(K + 1):
        if len(S) == 1:
            ans += pow(25, i, MOD) * pow(26, K - i, MOD)
        else:
            ans += pow(25, i, MOD) * cmb(i + len(S) - 1, len(S) - 1, MOD) * pow(26, K - i, MOD)

    print(ans % MOD)


if __name__ == '__main__':
    main()

Submission status: Runtime Error

Solution code:
import sys
import math
import collections

sys.setrecursionlimit(10 ** 8)

input = sys.stdin.readline


def main():
    K = int(input())
    S = input().strip()

    MOD = 10 ** 9 + 7

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

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

    N = 10 ** 6
    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)

    ans = 0
    for i in range(K + 1):
        ans += pow(25, i, MOD) * cmb(i + len(S) - 1, len(S) - 1, MOD) * pow(26, K - i, MOD)

    print(ans % MOD)


if __name__ == '__main__':
    main()