Java Assignment and Java Project.

Largest Gold Ingot TCS CodeVita 9 [SOLVED].

Ramesh is a goldsmith, who brought a large number of gold ingot each of different length(L) but equal breadth(B) and height(H). He wanted to wield the ingots of same length with each other.

Problem Description

Ramesh is a goldsmith, who brought a large number of gold ingot each of different length(L) but equal breadth(B) and height(H). He wants to weld the ingots of same length with each other. He tasks his new employee, Akash, to weld the ingots of same length with each other. But Akash forgot that he had to weld the ingots of same length, instead he welded the ingots in a random manner.

Later Ramesh found out what he had done. He then ordered Akash to cut the welded ingot such that a cuboid with the largest volume from the welded gold ingot is obtained.

Find the volume of summation of gold ingots minus volume of the largest cuboid.

Constraints

0 < G < 10^5

Input

First Line contains one integer G, denoting number of gold ingots

Second line contains two space separated integers B and H, where B denotes the breadth and H denotes the height of individual ingot

Third line contains G space separated integers, denoting the length of the individual gold ingots that are welded together in adjacent manner

Output

An integer corresponding to the volume of summation of gold ingots minus volume of the largest cuboid, mod 10^9+7.

Time Limit

Examples

Example 1

Input

1 1

6 7 3 4 5 1 3

Output

Explanation

Total volume of shaded region is 15 and the total volume is 29. So the volume of summation of gold ingots minus largest cuboid obtained is 14, since the height is 1 and breadth is 1.

Example 2

Input

1 2

1 2 6 4 5 3 4

Output

Explanation

The volume of summation of gold ingots minus largest cuboid obtained is 20, since the height is 2 and breadth is 1.

Solution in Java:-

import java.util.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

class LargestGoldIngot
{
   public static void main(String[] args) throws IOException {
   int n,i,sum=0, B,H,m,res=0,ans=0,peek;
   int arr[];

   Scanner sc=new Scanner(System.in);
   BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
     n=sc.nextInt();
     m=(int)Math.pow(10,9)+7;

         B=sc.nextInt();
         H=sc.nextInt();

   arr=new int[n];
   for( i=0;i<n;i++)
   {

      arr[i]=sc.nextInt();

       sum=sum+arr[i];

   }

   Stack<Integer> stack = new Stack<Integer>();
   for(i=0;i<n;i++){

       while(stack.empty()==false && arr[i]<=arr[stack.peek()]){

            peek=stack.peek();

           stack.pop();

           res= arr[peek]* (stack.empty()?i:(i-stack.peek()-1));

           ans=Math.max(ans%m,res);

       }

       stack.push(i);

   }

   while(stack.empty()==false){

        peek=stack.peek();

       stack.pop();

       res=arr[peek]*(stack.empty()? n:(n-stack.peek()-1));

       ans=Math.max(ans%m,res);


   }
   System.out.println(((sum%m-ans%m)%m*B%m*H%m)%m);
   }//end of main
}