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Maximum

Time Limit:3000MS     Memory Limit:0KB     64bit IO Format:%lld & %llu

Submit Status

Description

 

Let x₁, x₂,..., x_m be real numbers satisfying the following conditions:

a)

-x_i ;

b)

x₁ + x₂ +...+ x_m = b *  for some integers a and b (a > 0).

Determine the maximum value of x^p₁ + x^p₂ +...+ x^p_m for some even positive integer p.

Input

Each input line contains four integers: m, p, a, b ( m2000, p12, p is even). Input is correct, i.e. for each input numbers there existsx₁, x₂,..., x_m satisfying the given conditions.

Output

For each input line print one number - the maximum value of expression, given above. The answer must be rounded to the nearest integer.

Sample Input

1997 12 3 -318 
10 2 4 -1

Sample Output

189548 
6

#include<stdio.h>
#include<string.h>
#include<set>
#include<math.h>
#include<iostream>
#include<algorithm>
using namespace std;
int main()
{
    int m,p,a,b;
    double ans;
    while(~scanf("%d%d%d%d",&m,&p,&a,&b))
    {
        if(b<0)
            b=-b,ans=a*b*pow(sqrt(a*1.0)/a,p),m-=a*b;
        else ans=b*pow(sqrt(a*1.0),p),m-=b;
        int rr=m/(a+1);
        m%=(a+1);
        m--;
        ans+=rr*(pow(sqrt(a*1.0),p*1.0)+a*pow(sqrt(a*1.0)/a,p*1.0));
        if(m>0){
        ans+=m*pow(sqrt(a*1.0)/a,p);
        ans+=pow(m*sqrt(a*1.0)/a,p);
        }
        printf("%.0lf
",ans);
    }
}