Problem:
Score : 500 points

Problem Statement

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.

Constraints

1 \leq K \leq 10^5

2 \leq A_i \leq 10^9

All input values are integers.

Input

Input is given from Standard Input in the following format:

K
A_1 A_2 ... A_K

Output

Print two integers representing the smallest and the largest possible value of N, respectively,
or a single integer -1 if the described situation is impossible.

Sample Input 1

4
3 4 3 2

Sample Output 1

6 8

For example, if the game starts with 6 children, then it proceeds as follows:

In the first round, 6 children form 2 groups of 3 children, and nobody leaves the game.

In the second round, 6 children form 1 group of 4 children, and 2 children leave the game.

In the third round, 4 children form 1 group of 3 children, and 1 child leaves the game.

In the fourth round, 3 children form 1 group of 2 children, and 1 child leaves the game.

The last 2 children are declared the winners.

Sample Input 2

5
3 4 100 3 2

Sample Output 2

-1

This situation is impossible.
In particular, if the game starts with less than 100 children, everyone leaves after the third round.

Sample Input 3

10
2 2 2 2 2 2 2 2 2 2

Sample Output 3

2 3

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

import sys
readline = sys.stdin.readline

K = int(readline())
A = list(map(int,readline().split()))[::-1] # 逆から見ていくため反転

# 現在の数
cur = 2

if A[0] != 2: # 最後は必ず2
  print(-1)
  exit(0)

#print(A)

def getMinVal(c,a):
  # aの倍数でcより大きく最も小さい数を求める
  return (((c- 1) // a) + 1) * a

def getMaxVal(minval,a):
  # 算出済みのminvalを元に、取りうる最大の数（次の倍数より1小さいもの）を求める
  return minval + a - 1

# まず最小のほうを求める
for i in range(len(A)):
  # 現在のcurの値から起こりうる最小/最大値
  minpos = getMinVal(cur,A[i])
  maxpos = getMaxVal(minpos,A[i])
  
  if A[i] < minpos or maxpos < A[i]:
    print(-1)
    exit(0)

  # これが次の項目の倍数である必要がある。
  if i + 1 < len(A):
    if minpos % A[i + 1] != 0:
      cur = getMinVal(minpos,A[i + 1])
    else:
      cur = minpos
  else:
    cur = minpos
  

ans = [0] * 2
ans[0] = cur
  
def getNextMax(c,a):
  # cより小さい最も大きいaの倍数を返す
  return (c // a) * a
 
cur = 2
# 次に最大のほう
for i in range(len(A)):
  # 現在のcurの値から起こりうる最小/最大値
#  print("i",i,"A[i]",A[i])
  minpos = getMinVal(cur,A[i])
  maxpos = getMaxVal(minpos,A[i])
#  print("minpos",minpos,"maxpos",maxpos)
  if cur * 2 < A[i]:
    print(-1)
    exit(0)
  # 取りうる最大の数maxvalとしたいのだが、これが次のA[i+1]の倍数でなくてはいけない
  # 倍数でない場合は、maxvalより小さい最も大きい倍数である必要がある
  if i + 1 < len(A):
    if maxpos % A[i + 1] != 0:
      cur = getNextMax(maxpos,A[i + 1])
    else:
      cur = maxpos
  else:
    cur = maxpos
#  print("cur",cur)
    
ans[1] = cur

print(*ans)