Python

#!/bin/python3

import math
import os
import random
import re
import sys

sys.setrecursionlimit(20000)

#
# Complete the 'solve' function below.
#
# The function is expected to return a STRING.
# The function accepts following parameters:
#  1. LONG_INTEGER k
#  2. LONG_INTEGER n
#

def solve(k, n):
    # Write your code here
    if k == 1:
        return 1
    else:
        return k**n + solve(k-1, n)
        

if __name__ == '__main__':
    fptr = open(os.environ['OUTPUT_PATH'], 'w')

    t = int(input().strip())

    for t_itr in range(t):
        first_multiple_input = input().rstrip().split()

        k = int(first_multiple_input[0])

        n = int(first_multiple_input[1])

        result = solve(k, n)
        
        result = result % 100
        
        if result <10:
            strRes = "0"+str(result)
        else:
            strRes = str(result)
            
        fptr.write(strRes + '\n')

    fptr.close()

def atoNmodp(arra,N,p):
    if N==1:
        return arra
    if N&1:
        newa = atoNmodp(arra,N-1,p)
        return list(map(lambda x,y: x*y%p, newa, arra))
    else:
        newa = atoNmodp(arra,N>>1,p)
        return list(map(lambda x: x*x%p, newa))

def solve(k, n):
    
    allMod = atoNmodp(range(1,100),n,100)

    resMod =0
    res100 =0
    kmod100 =k%100
    for i, num in enumerate(allMod):
        res100 = res100 + num %100
        if i+1==kmod100:
            resMod =res100

    ret = str(((k//100%100) *res100 + resMod) %100)
    if len(ret) ==1:
        ret='0'+ret
    return ret