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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.math.BigInteger;
import java.sql.ClientInfoStatus;
import java.time.Year;
import java.util.*;
import java.util.concurrent.Executors;
import java.util.concurrent.ScheduledExecutorService;
import java.util.concurrent.TimeUnit;
import java.util.function.BiPredicate;
import java.util.function.Function;
import java.util.function.IntBinaryOperator;
import java.util.function.Predicate;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

import static java.lang.Math.*;
import static java.lang.String.format;

public class Main {
    public static void main(String[] args) {
        solve();
    }
    final static long INF= Long.MAX_VALUE>>2;
    final static int MOD = 1_000_000_007;
    final static int[] dx4 = { 0, 1, 0, -1 };
    final static int[] dy4 = { 1, 0, -1, 0 };
    final static int[] dx9 = {-1, -1, -1,  0,  0, 0, 1, 1,1};
    final static int[] dy9 = {-1, 0, 1, -1, 0, 1, -1, 0,1};
    final static Runnable me=()->{};
    static int id=1;
    public static void solve(){
        //TODO:Solve problem like ***
        Scanner sc=new Scanner();
        final int k = sc.nextInt();
        long[] a = new long[k];
        for (int i = 0; i < k; i++) {
            a[i] = sc.nextInt();
        }
        if(a[k-1]!=2){
            put(-1);
            return;
        }
        long[] x = new long[k];
        long[] y = new long[k];
        x[k - 1] = 2;
        y[k - 1] = 3;
        for (int i = k - 2; i >= 0; i--) {
//            put("x", Arrays.toString(x));
//            put("y", Arrays.toString(y));
            long modx = x[i + 1] % a[i];
            x[i] = x[i + 1]+((modx==0)?0:(a[i]-modx));
            if(x[i]>=x[i+1]+a[i+1]){
//                put("1:x[i]",x[i]);
                put(-1);
                return;
            }
            long mody = (x[i + 1]+a[i+1]-1) % a[i];
            long zeroy = x[i+1]+a[i+1] - 1 - mody;
            y[i] = zeroy+a[i];
            if(y[i]<x[i+1]){
//                put("2:y[i]", y[i]);
                put(-1);
                return;
            }
        }
//        put("x", Arrays.toString(x));
//        put("y", Arrays.toString(y));
        put(format("%d %d",x[0],y[0]-1));



    }
    static void set(int index,String s,int[] x){
        if(s.equals("Vacant")){
            System.exit(0);
        }else if(s.equals("Male")){
            x[index]=1;
        }else{
            x[index] = 2;
        }
    }

    static class Accepter<T>{
        private T val;
        private final Predicate p;
        public Accepter(T defaultValue,Predicate p){
            this.val=defaultValue;
            this.p=p;
        }

        /**
         * @return accepted newval?
         */
        public boolean replace(T newVal){
            if(p.test(newVal)){
                this.val=newVal;
                return true;
            }
            return false;
        }
    }
    //runWhenEAで使う
    private static Runnable func(Object... objects){
        try{
            assert false;
            return me;
        }catch(AssertionError e){
            return ()->{put(objects);};
        }
    }
    private static void print(Object... objects){
        if(objects.length==1){
            System.out.print(objects[0]);
        }else{
            System.out.print(Arrays.toString(objects));
        }
    }
    private static void put(Object... objects) {
        print(objects);
        put();
    }
    private static void put(){
        System.out.println();
    }


    private static void runWhenEA(Runnable runnable){
        try{
            assert false;
        }catch(AssertionError e){
            PrintStream ps=System.out;
            PrintStream pse=System.err;
            System.setOut(pse);
            runnable.run();
            System.setOut(ps);
        }
    }
    private static void putM(String name,char[][] mat){
        put("---------------------"+name+"-----------------");
        for (int i = 0; i < mat.length; i++) {
            put(Arrays.toString(mat[i]));
        }
    }
    private static void putM(String name,int[][] mat){
        put("---------------------"+name+"-----------------");
        for (int i = 0; i < mat.length; i++) {
            put(Arrays.toString(mat[i]));
        }
    }
    private static void putM(String name,long[][] mat){
        put("---------------------"+name+"-----------------");
        for (int i = 0; i < mat.length; i++) {
            put(Arrays.toString(mat[i]));
        }
    }
    private static void putM(String name,boolean[][] mat){
        put("---------------------"+name+"-----------------");
        for (int i = 0; i < mat.length; i++) {
            put(Arrays.toString(mat[i]));
        }
    }
    final static private class Scanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;

        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            } else {
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }

        private int readByte() {
            if (hasNextByte())
                return buffer[ptr++];
            else
                return -1;
        }

        private boolean isPrintableChar(int c) {
            return 33 <= c && c <= 126;
        }

        public boolean hasNext() {
            while (hasNextByte() && !isPrintableChar(buffer[ptr]))
                ptr++;
            return hasNextByte();
        }

        public String next() {
            if (!hasNext())
                throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while (isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        public long nextLong() {
            if (!hasNext())
                throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while (true) {
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                } else if (b == -1 || !isPrintableChar(b)) {
                    return minus ? -n : n;
                } else {
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }

        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
                throw new NumberFormatException();
            return (int) nl;
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
    static private class FixedIntPair {
        final public int x, y;
        final static public FixedIntPair ZEROS=new FixedIntPair(0,0);
        FixedIntPair(int x, int y) {
            this.x = x;
            this.y = y;
        }
        @Override
        public String toString() {
            return format(FixedIntPair.class.getSimpleName()+":(%d,%d)", x, y);
        }
    }
    final static private class FixedLongPair {
        final public long x, y;
        final static public FixedLongPair ZEROS=new FixedLongPair(0,0);
        FixedLongPair(long x, long y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public int hashCode() {
            return (int)x+(int)y;
        }

        @Override
        public boolean equals(Object obj) {
            if(obj==null)return false;
            if(!(obj instanceof FixedLongPair)) return false;
            FixedLongPair pair=(FixedLongPair)obj;
            return this.x==pair.x&&this.y==pair.y;
        }

        @Override
        public String toString() {
            return format(FixedLongPair.class.getSimpleName()+":(%d,%d)", x, y);
        }
    }
    final static private class Binary{
        public static String toZeroPadding(int i){
            return format("%"+Integer.toBinaryString(-1).length()+"s",Integer.toBinaryString(i)).replace(' ','0');
        }
        public static String toZeroPadding(long i){
            return format("%"+Long.toBinaryString(-1).length()+"s",Long.toBinaryString(i)).replace(' ','0');
        }
    }
    public static class BinaryIndexedTree {
        final int n;
        final long[] array;
        BinaryIndexedTree(long[] array){
            this.n=array.length;
            this.array=new long[n];
            for(int i=0;i<array.length;i++){
                add(i,array[i]);
            }
        }
        BinaryIndexedTree(int[] array){
            this.n=array.length;
            this.array=new long[n];
            for(int i=0;i<array.length;i++){
                add(i,array[i]);
            }
        }
        public void add(int index,long val){
            for(;index<n;index|=index+1){
                array[index]+=val;
            }
        }
        public long sum(int index){
            long result=0;
            for(;index>=0;index=(index&(index+1))-1){
                result+=array[index];
            }
            return result;
        }

        /**
         *
         * @param array arrayが1～nの順列になっていないならば定義されない
         * @return 転倒数
         */
        public static int inv(int[] array){
            int[] a=new int[array.length];
            BinaryIndexedTree bit=new BinaryIndexedTree(a);
            bit.add(array[0]-1,1);
            int result=0;
            for(int i=1;i<array.length;i++){
                System.out.println(bit);
                result+=i-bit.sum(array[i]-1);
                bit.add(array[i]-1,1);
            }
            return result;
        }

        @Override
        public String toString() {
            long[] array=new long[n];
            for(int i=0;i<n;i++){
                array[i]=sum(i);
            }
            String result="";
            result+="ruiseki:"+ Arrays.toString(array)+"\n";
            array[0]=sum(0);
            for(int i=1;i<n;i++){
                array[i]=sum(i)-sum(i-1);
            }
            result+="source::"+Arrays.toString(array);
            return result;
        }
    }

    final static private class Util {
        static long gcd(long a,long b){
            a= abs(a);
            b= abs(b);
            if(a<b){
                long tmp=a;
                a=b;
                b=tmp;
            }
            while(b!=0){
                long r=a%b;
                a=b;
                b=r;
            }
            return a;
        }
        static int gcd(int a,int b){
            a= abs(a);
            b= abs(b);
            if(a<b){
                int tmp=a;
                a=b;
                b=tmp;
            }
            while(b!=0){
                int r=a%b;
                a=b;
                b=r;
            }
            return a;
        }
        static long lcm(long a,long b){
            long gcd=gcd(a,b);
            long result=b/gcd;
            return a*result;
        }
        static boolean isValidCell(int i,int j,int h,int w){
            return i>=0&&i<h&&j>=0&&j<w;
        }
    }
}































































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