Problem:
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You are given $n$ packages of $w_i$ kg from a belt conveyor in order ($i = 0, 1, ... n-1$). You should load all packages onto $k$ trucks which have the common maximum load $P$. Each truck can load consecutive packages (more than or equals to zero) from the belt conveyor unless the total weights of the packages in the sequence does not exceed the maximum load $P$.

Write a program which reads $n$, $k$ and $w_i$, and reports the minimum value of the maximum load $P$ to load all packages from the belt conveyor.

Input

In the first line, two integers $n$ and $k$ are given separated by a space character. In the following $n$ lines, $w_i$ are given respectively.

Output

Print the minimum value of $P$ in a line.

Constraints

$1 \leq n \leq 100,000$

$1 \leq k \leq 100,000$

$1 \leq w_i \leq 10,000$

Sample Input 1

5 3
8
1
7
3
9

Sample Output 1

10

If the first truck loads two packages of $\{8, 1\}$, the second truck loads two packages of $\{7, 3\}$ and the third truck loads a package of $\{9\}$, then the minimum value of the maximum load $P$ shall be 10.

Sample Input 2

4 2
1
2
2
6

Sample Output 2

6

If the first truck loads three packages of $\{1, 2, 2\}$ and the second truck loads a package of $\{6\}$, then the minimum value of the maximum load $P$ shall be 6.

Solution in C (judge verdict: Time Limit Exceeded)

#include <stdio.h>
 
#define _U  unsigned
 
#define NUM_OF_PACKAGES_MAX 100000
#define NUM_OF_TRUCKS_MAX   100000
 
int main(void)
{    
    _U int      loop_cnt_1          = 0;
    _U int      loop_cnt_2          = 0;
    _U int      num_of_packages     = 0;
    _U int      num_of_trucks       = 0;
    _U int      max_load            = 0;
     
    _U short    packages_weight[NUM_OF_PACKAGES_MAX]    = {};
     
    _U short    ref_packages_weight = 0;
    _U short    ref_offset          = 1;
    _U int      sum_weight          = 0;
     
    _U int      trucks_load[NUM_OF_TRUCKS_MAX]          = {};
    _U short    next_package[NUM_OF_TRUCKS_MAX]         = {};
    _U int      total_load_weight   = 0;
    
    /* get number of packages and trucks */
    scanf("%d %d", &num_of_packages, &num_of_trucks);
    
    /* get packages weight and calculate sum weight */
    for(loop_cnt_1 = 0; loop_cnt_1 < num_of_packages; loop_cnt_1++){
         
        scanf("%d", &packages_weight[loop_cnt_1]);
        sum_weight += packages_weight[loop_cnt_1];
        
    }
     
    /* calculate average trucks load */
    ref_packages_weight = (sum_weight / num_of_trucks) + 1;
    
    //printf("ref = %d\n\n", ref_packages_weight);
    
    loop_cnt_1 = 0; 
    while(loop_cnt_1 < num_of_trucks){
         
        while(loop_cnt_2 < num_of_packages){
             
            /* check over load */
            if(ref_packages_weight < (trucks_load[loop_cnt_1] + packages_weight[loop_cnt_2])){
                 
                break;
                 
            }
                
                 
            trucks_load[loop_cnt_1] += packages_weight[loop_cnt_2];

            //printf("%d ", packages_weight[loop_cnt_2]); 
             
            loop_cnt_2++;
        }
        
        if(max_load < trucks_load[loop_cnt_1]){
             
            max_load = trucks_load[loop_cnt_1];
             
        }
        
        total_load_weight += trucks_load[loop_cnt_1];
         
        //printf("\nload = %d\n", trucks_load[loop_cnt_1]);
         
        next_package[loop_cnt_1] = loop_cnt_2;
         
        loop_cnt_1++;
         
    }
    
    while(total_load_weight < sum_weight){
        
        //printf("total %d sum %d reload\n\n", total_load_weight, sum_weight);
        ref_packages_weight++;
        
        //printf("ref = %d\n", ref_packages_weight);
        
        loop_cnt_1 = 0; 
        while(loop_cnt_1 < num_of_trucks){
            
            while(next_package[loop_cnt_1] < num_of_packages){
                if(ref_packages_weight >= (trucks_load[loop_cnt_1] + packages_weight[next_package[loop_cnt_1]])){
                    
                    trucks_load[loop_cnt_1] += packages_weight[next_package[loop_cnt_1]];
                    
                    if(loop_cnt_1 != num_of_trucks - 1){
                        
                        trucks_load[loop_cnt_1 + 1] -= packages_weight[next_package[loop_cnt_1]];
                        next_package[loop_cnt_1]++;
                        
                    }else{
                        
                        total_load_weight += packages_weight[next_package[loop_cnt_1]];
                        next_package[loop_cnt_1]++;
                    
                    }
                        
                    //printf("%d ", packages_weight[next_package[loop_cnt_1]]);
                    
                }else{
                    
                    break;
                    
                }
                
            }
            
            if(max_load < trucks_load[loop_cnt_1]){
             
                max_load = trucks_load[loop_cnt_1];
                 
            }
            
            //printf("\nload = %d\n", trucks_load[loop_cnt_1]);
            
            loop_cnt_1++;
            
        }
        
        //printf("\nload = %d\n", trucks_load[loop_cnt_1]);
        
    }
     
    printf("%d\n", max_load);
     
    return 0;
}