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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<vector>
#include<map>
#include<set>
#include<algorithm>
#include<numeric>
#include<limits>
#include<bitset>
#include<functional>
#include<type_traits>
#include<queue>
#include<stack>
#include<array>
#include<random>

namespace lib
{
	template<std::uint64_t Mod>struct modnum;
	template<class T>constexpr T pow(T base, std::size_t p)
	{
		if (p == 0)
		{
			return T(1);
		}
		else if (p == 1)
		{
			return base;
		}
		else if (p == 2)
		{
			return base * base;
		}
		else if (p % 2 == 0)
		{
			return pow(pow(base, p / 2), 2);
		}
		else
		{
			return pow(pow(base, p / 2), 2)*base;
		}
	}
	template<std::uint64_t Mod>constexpr auto inverse(modnum<Mod> const&);

	template<std::uint64_t Mod>struct modnum
	{
		static constexpr auto mod = Mod;
		std::uint64_t val;
		modnum() = default;
		constexpr modnum(std::uint64_t v):val(v%Mod)
		{

		}

		constexpr modnum& operator+=(modnum const& v)
		{
			val += v.val;
			val %= mod;
			return *this;
		}
		constexpr modnum& operator-=(modnum const& v)
		{
			val += mod - v.val;
			val %= mod;
			return *this;
		}
		constexpr modnum& operator*=(modnum const& v)
		{
			val *= v.val;
			val %= mod;
			return *this;
		}
		constexpr modnum& operator/=(modnum const& v)
		{
			return operator*=(inverse(v));
		}
	};
	template<std::uint64_t Mod>constexpr auto operator+(modnum<Mod> lhs, modnum<Mod>const& rhs)
	{
		return lhs += rhs;
	}
	template<std::uint64_t Mod>constexpr auto operator-(modnum<Mod> lhs, modnum<Mod>const& rhs)
	{
		return lhs -= rhs;
	}
	template<std::uint64_t Mod>constexpr auto operator*(modnum<Mod> lhs, modnum<Mod>const& rhs)
	{
		return lhs *= rhs;
	}
	template<std::uint64_t Mod>constexpr auto operator/(modnum<Mod> lhs, modnum<Mod>const& rhs)
	{
		return lhs /= rhs;
	}

	template<std::uint64_t Mod>constexpr auto inverse(modnum<Mod>const& base)
	{
		return pow(base, Mod - 2);
	}

	template<class T>constexpr auto clamp(T v)
	{
		return std::max(v, T());
	}
	template<class T>void sort(T& vec)
	{
		std::sort(vec.begin(), vec.end());
	}
	template<class T, class Compare>void sort(T& vec, Compare&& compare)
	{
		std::sort(vec.begin(), vec.end(), std::forward<Compare>(compare));
	}


	template<class T>auto lower_bound(std::vector<T>const& vec, T v)
	{
		return std::distance(vec.begin(), std::lower_bound(vec.begin(), vec.end(), v));
	}
	template<class T>auto upper_bound(std::vector<T>const& vec, T v)
	{
		return std::distance(vec.begin(), std::upper_bound(vec.begin(), vec.end(), v));
	}

	struct scope_exit
	{
		std::function<void(void)> func;
		scope_exit(std::function<void(void)> f):func(f)
		{

		}
		~scope_exit()
		{
			func();
		}
	};

	template<int val>using int_tag = std::integral_constant<int, val>;

	template<class Return, class Argument>struct minimam_searcher
	{
		Return operator()(std::function<Return(Argument)> func, Argument beg, Argument end)const
		{
			Return min = std::numeric_limits<Return>::max();
			for (; beg != end; ++beg)
			{
				min = std::min(min, func(beg));
			}
			return min;
		}
	};
	template<class Return, class Argument>constexpr minimam_searcher<Return, Argument> minimam{};

	template<class T>T gcd(T a, T b)
	{
		if (a > b)
		{
			return gcd(b, a);
		}
		if (a == T())
		{
			return b;
		}
		return gcd(b%a, a);
	}

	static constexpr std::int64_t intlog2(std::int64_t x)
	{
		for (std::int64_t i = 0, j = 2; i < 64; ++i, j <<= 1)
		{
			if (j > x)
			{
				return i;
			}
		}
		return 64;
	}

	struct segtree
	{
		std::vector<std::int64_t> tree;
		std::size_t depth_;
		segtree(std::size_t depth):tree(std::size_t(1) << (depth + 1)), depth_(depth)
		{

		}

		void change(std::size_t index, std::int64_t val)
		{
			change(index, val, 0);
		}

		std::int64_t get(std::size_t left, std::size_t right)//[left, right]の範囲
		{
			return get(left, right + 1, 0, 1, 0);
		}

		void increment(std::size_t index)
		{
			increment(index, 0);
		}

		void decrement(std::size_t index)
		{
			decrement(index, 0);
		}
	private:
		std::int64_t change(std::size_t index, std::int64_t val, std::size_t dep)
		{
			auto shift = std::size_t(1) << dep;
			auto s = std::size_t(1) << (depth_ - dep);
			if (dep == depth_)
			{
				std::swap(tree[shift + index / s - 1], val);
				return val;
			}
			else
			{
				auto v = change(index, val, dep + 1);
				tree[shift + index / s - 1] += val - v;
				return v;
			}
		}

		std::int64_t get(std::size_t a, std::size_t b, std::size_t left, std::size_t right, std::size_t dep)
		{
			auto lshift = left << (depth_ - dep);
			auto rshift = right << (depth_ - dep);
			if (a <= lshift && rshift <= b)
			{
				return tree[(std::size_t(1) << dep) + left - 1];
			}
			else if (rshift <= a || b <= lshift)
			{
				return 0;
			}
			else
			{
				return
					get(a, b, left << 1, left + right, dep + 1) +
					get(a, b, left + right, right << 1, dep + 1);
			}
		}

		void increment(std::size_t index, std::size_t dep)
		{
			auto shift = std::size_t(1) << dep;
			auto s = std::size_t(1) << (depth_ - dep);
			++tree[shift + index / s - 1];
			if (dep != depth_)
			{
				increment(index, dep + 1);
			}
		}

		void decrement(std::size_t index, std::size_t dep)
		{
			auto shift = std::size_t(1) << dep;
			auto s = std::size_t(1) << (depth_ - dep);
			--tree[shift + index / s - 1];
			if (dep != depth_)
			{
				decrement(index, dep + 1);
			}
		}
	};
	template<class T, int N>class binary_indexed_tree
	{
		std::array<T, N> ar;
	public:
		binary_indexed_tree(T val = 0)//全ての要素をvalで初期化する
			:ar{}
		{
			for (int i = 1; i <= N; ++i)
			{
				ar[i - 1] = (i&-i)*val;
			}
		}
		void add(T val, int index)//index番の要素にvalを足す
		{
			++index;
			for (; index <= N; index += index & -index)
			{
				ar[index - 1] += val;
			}
		}
		T get(int index)const//0からindex番までの要素の和を返す
		{
			T ret{};
			for (++index; index > 0; index -= index & -index)
			{
				ret += ar[index - 1];
			}
			return ret;
		}
	};

	template<class T>using p_queue = std::priority_queue<T, std::vector<T>, std::greater<>>;

	template<class T>auto max(std::vector<T>const& vec)
	{
		return *std::max_element(vec.begin(), vec.end());
	}
	template<class T>auto min(std::vector<T>const& vec)
	{
		return *std::min_element(vec.begin(), vec.end());
	}
}

namespace std
{
	template<std::uint64_t Mod>decltype(auto) operator<<(ostream& ost, lib::modnum<Mod>const& v)
	{
		return ost << v.val;
	}
}

void Main();
int main()
{
	std::cin.tie(nullptr);
	std::cin.sync_with_stdio(false);
	Main();
}

typedef lib::modnum<1000000007> mod_t;


void Main()
{
	int K;
	std::cin >> K;
	std::vector<int> round(K);
	for (auto& v : round)
	{
		std::cin >> v;
	}
	int min = 2, max = 2;
	for (int i = K; i > 0; --i)
	{
		int a = (max / round[i - 1])*round[i - 1];
		if (min <= a && a <= max)
		{
			min = a;
			max = a + round[i - 1] - 1;
		}
		else
		{
			std::cout << -1 << std::endl;
			return;
		}
	}
	std::cout << min << " " << max << std::endl;
}