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: Accepted)

#include <stdio.h>
#include <string.h>
#include <stdlib.h>

#define BUF_SIZE 30

// size: specify sizeof(str)
int get_str(char *str, int size) {
    if(!fgets(str, size, stdin)) return -1;
    return 0;
}

int get_int(void) {
  int num;
#ifdef BUF_SIZE
  char line[BUF_SIZE];
  if(!fgets(line, BUF_SIZE, stdin)) return 0;
  sscanf(line, "%d", &num);
#else
#error
#endif
  return num;
}

int get_int2(int *a1, int *a2) {
#ifdef BUF_SIZE
  char line[BUF_SIZE];
  if(!fgets(line, BUF_SIZE, stdin)) return -1;
  sscanf(line, "%d %d", a1, a2);
#else
#error
#endif
  return 0;
}
#define PACKS_MAX 100000
#define TRACKS_MAX 100000

int desc(const void *a, const void *b) {
    return *(int*)b - *(int*)a;
}

int asc(const void *a, const void *b) {
    return *(int*)a - *(int*)b;
}

int judge(int *cum, int size, int tracks, int key) {
    int cnt;
    int prev = 0;
    for(cnt = 0; cnt < tracks; cnt++) {
        int low = prev-1;
        int high = size;
        while(low + 1 < high) {
            int mid = (low+high)/2;
            // [prev, mid)
            int rsum = cum[mid] - cum[prev];
            // upper bound
            if(rsum <= key) {
                low = mid;
            } else {
                high = mid;
            }
        }
        prev = low;
        // no packages
        if(prev == size-1) break;
#ifdef DEBUG
        printf("prev: %d\n", prev);
#endif
    }
    return (prev == size-1);
}

#define max(a,b) ((a) > (b) ? (a) : (b))

int main(void) {
    int ps, tracks;
    get_int2(&ps, &tracks);
    int i;
    int low = 0;
    static int cum[PACKS_MAX+1];
    for(i = 1; i <= ps; i++) {
        int p = get_int();
        cum[i] = cum[i-1] + p;
        low = max(low, p);
    }

    int high = cum[ps];
    low--; high++;
    // binary-search
    while(low + 1 < high) {
        int mid = (low + high)/2;
        // lower bound
        if(judge(cum, ps+1, tracks, mid)) {
            high = mid;
        } else {
            low = mid;
        }
    }
    printf("%d\n", high);
    return 0;
}