CodeForces Round #515 Div.3 D. Boxes Packing

http://codeforces.com/contest/1066/problem/D

Maksim has $\mathrm{nn objects\; and mm boxes,\; each\; box\; has\; size\; exactly kk.\; Objects\; are\; numbered\; from 11 to nn in\; order\; from\; left\; to\; right,\; the\; size\; of\; the ii-th\; object\; is aiai.}$

Maksim wants to pack his objects into the boxes and he will pack objects by the following algorithm: he takes one of the empty boxes he has, goes from left to right through the objects, and if the $\mathrm{ii-th\; object\; fits\; in\; the\; current\; box\; (the\; remaining\; size\; of\; the\; box\; is\; greater\; than\; or\; equal\; to aiai),\; he\; puts\; it\; in\; the\; box,\; and\; the\; remaining\; size\; of\; the\; box\; decreases\; by aiai.\; Otherwise\; he\; takes\; the\; new\; empty\; box\; and\; continues\; the\; process\; above.\; If\; he\; has\; no\; empty\; boxes\; and\; there\; is\; at\; least\; one\; object\; not\; in\; some\; box\; then\; Maksim\; cannot\; pack\; the\; chosen\; set\; of\; objects.}$

Maksim wants to know the maximum number of objects he can pack by the algorithm above. To reach this target, he will throw out the leftmost object from the set until the remaining set of objects can be packed in boxes he has. Your task is to say the maximum number of objects Maksim can pack in boxes he has.

Each time when Maksim tries to pack the objects into the boxes, he will make empty all the boxes he has before do it (and the relative order of the remaining set of objects will not change).

Input

The first line of the input contains three integers $\mathrm{nn, mm, kk (1\le n,m\le 2\cdot 1051\le n,m\le 2\cdot 105, 1\le k\le 1091\le k\le 109)\; —\; the\; number\; of\; objects,\; the\; number\; of\; boxes\; and\; the\; size\; of\; each\; box.}$

The second line of the input contains $\mathrm{nn integers a1,a2,\dots ,ana1,a2,\dots ,an (1\le ai\le k1\le ai\le k),\; where aiai is\; the\; size\; of\; the ii-th\; object.}$

Output

Print the maximum number of objects Maksim can pack using the algorithm described in the problem statement.

Examples

input

Copy

5 2 6
5 2 1 4 2

output

Copy

4

input

Copy

5 1 4
4 2 3 4 1

output

Copy

1

input

Copy

5 3 3
1 2 3 1 1

output

Copy

5

Note

In the first example Maksim can pack only $\mathrm{44 objects.\; Firstly,\; he\; tries\; to\; pack\; all\; the 55 objects.\; Distribution\; of\; objects\; will\; be [5],[2,1][5],[2,1].\; Maxim\; cannot\; pack\; the\; next\; object\; in\; the\; second\; box\; and\; he\; has\; no\; more\; empty\; boxes\; at\; all.\; Next\; he\; will\; throw\; out\; the\; first\; object\; and\; the\; objects\; distribution\; will\; be [2,1],[4,2][2,1],[4,2].\; So\; the\; answer\; is 44.}$

In the second example it is obvious that Maksim cannot pack all the objects starting from first, second, third and fourth (in all these cases the distribution of objects is $[4][4]),\; but\; he\; can\; pack\; the\; last\; object\; ([1][1]).$

In the third example Maksim can pack all the objects he has. The distribution will be $[1,2],[3],[1,1][1,2],[3],[1,1].$

#include <bits/stdc++.h>
using namespace std;

const int maxn = 2e5 + 10;
int N, M, K;
int a[maxn];

int main() {
    scanf("%d%d%d", &N, &M, &K);
    for(int i = 1; i <= N; i ++)
        scanf("%d", &a[i]);
    int cnt = 0;
    int ans = K;
    for(int i = N; i >= 1; i --) {
        if(a[i] <= ans) {
            ans -= a[i];
            cnt ++;
        } else {
            M --;
            if(!M) break;
            ans = K - a[i];
            cnt ++;
        }
    }
    printf("%d
", cnt);
    return 0;
}