Problem: An adult game master and N children are playing a game on an ice rink. The game consists of K rounds. In the i-th round, the game master announces:    * Form groups consisting of A_i children each!  Then the children who are still in the game form as many groups of A_i children as possible. One child may belong to at most one group. Those who are left without a group leave the game. The others proceed to the next round. Note that it's possible that nobody leaves the game in some round.  In the end, after the K-th round, there are exactly two children left, and they are declared the winners.  You have heard the values of A_1, A_2, ..., A_K. You don't know N, but you want to estimate it.  Find the smallest and the largest possible number of children in the game before the start, or determine that no valid values of N exist.

Submission attempts (in order):

import numpy as np
import sys
sys.setrecursionlimit(100000)



def acinput():
    return list(map(int, input().split(" ")))



directions=np.array([[1,0],[0,1],[-1,0],[0,-1]])
directions = list(map(np.array, directions))

mod = 10**9+7


def factorial(n):
    fact = 1
    for integer in range(1, n + 1):
        fact *= integer
    return fact



def serch(x, count):
    #print("top", x, count)
            

    for d in directions:
        nx = d+x
        #print(nx)
        if np.all(0 <= nx) and np.all(nx < (H, W)):
            if field[nx[0]][nx[1]] == "E":
                count += 1 
                field[nx[0]][nx[1]] = "V"
                count = serch(nx, count)  
                continue
            if field[nx[0]][nx[1]] == "#":
                field[nx[0]][nx[1]] = "V"
                count = serch(nx, count)    
                 
    return count

def f(x):
    for i in range(K):
        x = x-x % A[i]
    return x

def bisect_search(f,val=0,l=0,r=10**6):

    #is_increase=(f(r)-f(l))>=0

    eps=10**(-5)
    while True:

        c=(l+r)//2
        print(l,c,r)
        input()
        if f(c)==val and f(c-1)!=val:
            return c
        #if f(c)-val < eps:
        #    return c

        if f(c)>val:
            r=c

        else:
            l=c
        
        if l==r:
            return False

def bisect_search_int(f,val=0,l=0,r=10**6,equal=False):
    #is_increase=(f(r)-f(l))>=0
    
    eps=10**(-5)
    if not equal:
        siki = "f(c) > val"
    else:
        siki = "f(c) >= val"

    while r-l>1:

        c=(l+r)//2
        
        if eval(siki,{"c":c,"f":f,"val":val}):
            r=c            
        else:
            l=c
        
        #if l==r:
        #    return False
    if f(l)!= f(c) and f(r)!=f(c):
        return False
    return l,r



K=int(input())
A=acinput()

r = 2+K*max(A)

l,r=bisect_search_int(f, 2,0,r,equal=True)
if f(l)==2:
    resL=l
elif f(r)==2:
    resL=r
else:
    resL=False

l, r = bisect_search_int(f, 2,0,r,equal=False)
if f(l) == 2:
    resR = l
elif f(r) == 2:
    resR = r
else:
    resR = False

if resL and resR:
    print(resL,resR)
else:
    print(-1)


#for x in range(0,20):
#    print(x,f(x))



import numpy as np
import sys
sys.setrecursionlimit(100000)



def acinput():
    return list(map(int, input().split(" ")))



directions=np.array([[1,0],[0,1],[-1,0],[0,-1]])
directions = list(map(np.array, directions))

mod = 10**9+7


def factorial(n):
    fact = 1
    for integer in range(1, n + 1):
        fact *= integer
    return fact



def serch(x, count):
    #print("top", x, count)
            

    for d in directions:
        nx = d+x
        #print(nx)
        if np.all(0 <= nx) and np.all(nx < (H, W)):
            if field[nx[0]][nx[1]] == "E":
                count += 1 
                field[nx[0]][nx[1]] = "V"
                count = serch(nx, count)  
                continue
            if field[nx[0]][nx[1]] == "#":
                field[nx[0]][nx[1]] = "V"
                count = serch(nx, count)    
                 
    return count

def f(x):
    for i in range(K):
        x = x-x % A[i]
    return x

def bisect_search(f,val=0,l=0,r=10**6):

    #is_increase=(f(r)-f(l))>=0

    eps=10**(-5)
    while True:

        c=(l+r)//2
        print(l,c,r)
        input()
        if f(c)==val and f(c-1)!=val:
            return c
        #if f(c)-val < eps:
        #    return c

        if f(c)>val:
            r=c

        else:
            l=c
        
        if l==r:
            return False

def bisect_search_int(f,val=0,l=0,r=10**6,equal=False):
    #is_increase=(f(r)-f(l))>=0
    
    eps=10**(-5)
    if not equal:
        siki = "f(c) > val"
    else:
        siki = "f(c) >= val"

    while r-l>1:

        c=(l+r)//2
        
        if eval(siki,{"c":c,"f":f,"val":val}):
            r=c            
        else:
            l=c
        
        #if l==r:
        #    return False
    if f(l)!= f(c) and f(r)!=f(c):
        return False
    return l,r



K=int(input())
A=acinput()

R = 2+K*max(A)
#R=10**6

l,r=bisect_search_int(f, 2,0,R,equal=True)
if f(l)==2:
    resL=l
elif f(r)==2:
    resL=r
else:
    resL=-1

l, r = bisect_search_int(f, 2,0,R,equal=False)
#print(l,r,f(l),f(r))
if f(l) == 2:
    resR = l
elif f(r) == 2:
    resR = r
else:
    resR = -1

if resL>=0:
    print(resL,resR)
else:
    print(-1)


#for x in range(0,20):
#    print(x,f(x))


Verdicts: Wrong Answer

Accepted