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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace Program
{
    public class AGC020B
    {
        static public void Solve()
        {
            var K = NextInt;
            var Alist = NextLongList(K);
            var minN = 2L;
            var maxN = 2L;

            Alist.Reverse();
            foreach (var item in Alist)
            {
                minN = ((minN - 1) / item + 1) * item;
                maxN = (maxN / item) * item + item - 1;
                if (minN > maxN)
                {
                    Console.WriteLine(-1);
                    return;
                }
            }

            Console.WriteLine(minN + " " + maxN);
        }

        static public void Main(string[] args)
        {
            if (args.Length == 0)
            {
                var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
                Console.SetOut(sw);
            }
            Solve();
            Console.Out.Flush();
        }
        static class Console_
        {
            private static Queue<string> param = new Queue<string>();
            public static string NextString()
            {
                if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item);
                return param.Dequeue();
            }
        }
        static int NextInt => int.Parse(Console_.NextString());
        static long NextLong => long.Parse(Console_.NextString());
        static double NextDouble => double.Parse(Console_.NextString());
        static string NextString => Console_.NextString();
        static List<int> NextIntList(int N) => Enumerable.Repeat(0, N).Select(_ => NextInt).ToList();
        static List<long> NextLongList(int N) => Enumerable.Repeat(0, N).Select(_ => NextLong).ToList();
        static List<double> NextDoubleList(int N) => Enumerable.Repeat(0, N).Select(_ => NextDouble).ToList();
        static List<string> NextStringList(int N) => Enumerable.Repeat(0, N).Select(_ => NextString).ToList();
        static List<T> Sort<T>(List<T> l) where T : IComparable
        {
            var tmp = l.ToArray(); Array.Sort(tmp); return tmp.ToList();
        }
        static List<T> RevSort<T>(List<T> l) where T : IComparable
        {
            var tmp = l.ToArray(); Array.Sort(tmp, (x, y) => y.CompareTo(x)); return tmp.ToList();
        }
        static IEnumerable<long> Prime(long x)
        {
            if (x < 2) yield break;
            yield return 2;
            var halfx = x / 2;
            var table = new bool[halfx + 1];
            var max = (long)(Math.Sqrt(x) / 2);
            for (long i = 1; i <= max; ++i)
            {
                if (table[i]) continue;
                var add = 2 * i + 1;
                yield return add;
                for (long j = 2 * i * (i + 1); j <= halfx; j += add) table[j] = true;
            }
            for (long i = max + 1; i <= halfx; ++i) if (!table[i]) yield return 2 * i + 1;
        }
        static IEnumerable<long> Divisor(long x)
        {
            if (x < 1) yield break;
            var max = (long)Math.Sqrt(x);
            for (long i = 1; i < max; ++i)
            {
                if (x % i != 0) continue;
                yield return i;
                if (i != x / i) yield return x / i;
            }
        }
        static long GCD(long a, long b)
        {
            while (b > 0) { var tmp = b; b = a % b; a = tmp; }
            return a;
        }
        class PQ<T> where T : IComparable
        {
            private List<T> h;
            private Comparison<T> c;
            public PQ(int cap, Comparison<T> c, bool asc = true) { h = new List<T>(cap); this.c = asc ? c : (x, y) => c(y, x); }
            public PQ(Comparison<T> c, bool asc = true) { h = new List<T>(); this.c = asc ? c : (x, y) => c(y, x); }
            public PQ(int cap, bool asc = true) : this(cap, (x, y) => x.CompareTo(y), asc) { }
            public PQ(bool asc = true) : this((x, y) => x.CompareTo(y), asc) { }
            public void Push(T v)
            {
                var i = h.Count;
                h.Add(v);
                while (i > 0)
                {
                    var ni = (i - 1) / 2;
                    if (c(v, h[ni]) >= 0) break;
                    h[i] = h[ni]; i = ni;
                }
                h[i] = v;
            }
            public T Peek => h[0];
            public int Count => h.Count;
            public T Pop()
            {
                var r = h[0];
                var v = h[h.Count - 1];
                h.RemoveAt(h.Count - 1);
                if (h.Count == 0) return r;
                var i = 0;
                while (i * 2 + 1 < h.Count)
                {
                    var i1 = i * 2 + 1;
                    var i2 = i * 2 + 2;
                    if (i2 < h.Count && c(h[i1], h[i2]) > 0) i1 = i2;
                    if (c(v, h[i1]) <= 0) break;
                    h[i] = h[i1]; i = i1;
                }
                h[i] = v;
                return r;
            }
        }
        class PQ<TKey, TValue> where TKey : IComparable
        {
            private PQ<Tuple<TKey, TValue>> q;
            public PQ(int cap, Comparison<TKey> c, bool asc = true) { q = new PQ<Tuple<TKey, TValue>>(cap, (x, y) => c(x.Item1, y.Item1), asc); }
            public PQ(Comparison<TKey> c, bool asc = true) { q = new PQ<Tuple<TKey, TValue>>((x, y) => c(x.Item1, y.Item1), asc); }
            public PQ(int cap, bool asc = true) : this(cap, (x, y) => x.CompareTo(y), asc) { }
            public PQ(bool asc = true) : this((x, y) => x.CompareTo(y), asc) { }
            public void Push(TKey k, TValue v) => q.Push(Tuple.Create(k, v));
            public Tuple<TKey, TValue> Peek => q.Peek;
            public int Count => q.Count;
            public Tuple<TKey, TValue> Pop() => q.Pop();
        }
        class Mod
        {
            static public long _mod = 1000000007;
            private long _val = 0;
            public Mod(long x) { _val = x; }
            static public implicit operator Mod(long x) => new Mod(x);
            static public explicit operator long(Mod x) => x._val;
            static public Mod operator +(Mod x) => x._val;
            static public Mod operator -(Mod x) => -x._val;
            static public Mod operator ++(Mod x) => x._val + 1;
            static public Mod operator --(Mod x) => x._val - 1;
            static public Mod operator +(Mod x, Mod y) => (x._val + y._val) % _mod;
            static public Mod operator -(Mod x, Mod y) => ((((x._val - y._val) % _mod) + _mod) % _mod);
            static public Mod operator *(Mod x, Mod y) => (x._val * y._val) % _mod;
            static public Mod operator /(Mod x, Mod y) => (x._val * Inverse(y._val)) % _mod;
            static public bool operator ==(Mod x, Mod y) => x._val == y._val;
            static public bool operator !=(Mod x, Mod y) => x._val != y._val;
            static public bool operator <(Mod x, Mod y) => x._val < y._val;
            static public bool operator >(Mod x, Mod y) => x._val > y._val;
            static public bool operator <=(Mod x, Mod y) => x._val <= y._val;
            static public bool operator >=(Mod x, Mod y) => x._val >= y._val;
            static public Mod Pow(Mod x, long y)
            {
                Mod a = 1;
                while (y != 0)
                {
                    if ((y & 1) == 1) a *= x;
                    x *= x;
                    y >>= 1;
                }
                return a;
            }
            static public long Inverse(long x)
            {
                long b = _mod, r = 1, u = 0, t = 0;
                while (b > 0)
                {
                    var q = x / b;
                    t = u; u = r - q * u; r = t;
                    t = b; b = x - q * b; x = t;
                }
                return r < 0 ? r + _mod : r;
            }
            override public bool Equals(object obj) => obj == null ? false : _val == ((Mod)obj)._val;
            public bool Equals(Mod obj) => obj == null ? false : _val == obj._val;
            public override int GetHashCode() => _val.GetHashCode();
            public override string ToString() => _val.ToString();
            static private List<Mod> _fact = new List<Mod>();
            static private List<Mod> _ifact = new List<Mod>();
            static private void Build(int n)
            {
                if (n >= _fact.Count)
                    for (int i = _fact.Count; i <= n; ++i)
                        if (i == 0L) { _fact.Add(1); _ifact.Add(1); }
                        else { _fact.Add(_fact[i - 1] * i); _ifact.Add(_ifact[i - 1] * Mod.Pow(i, _mod - 2)); }
            }
            static public Mod Comb(int n, int k)
            {
                Build(n);
                if (n == 0 && k == 0) return 1;
                if (n < k || n < 0) return 0;
                return _ifact[n - k] * _ifact[k] * _fact[n];
            }
        }
        static private List<long> _fact = new List<long>();
        static private void Build(int n)
        {
            if (n >= _fact.Count)
                for (int i = _fact.Count; i <= n; ++i)
                    if (i == 0L) _fact.Add(1);
                    else _fact.Add(_fact[i - 1] * i);
        }
        static public long Comb(int n, int k)
        {
            Build(n);
            if (n == 0 && k == 0) return 1;
            if (n < k || n < 0) return 0;
            return _fact[n] / _fact[k] / _fact[n - k];
        }
    }
}