Boxes Packing

### 题目描述 有 $n$ 个物品，$m$ 个盒子。其中第 $i$ 个物品的大小为 $a_i$，所有盒子的大小均为 $k$。Makmis 先生想要将这些物品放入盒子中。对于每个物品，如果可以放入当前盒子中则放入当前盒子，否则换一个新的盒子放入。如果物品数量太多使得盒子装不下，可以**将先放入的物品丢弃**。求出最多能够放入多少物品。 ### 输入格式 第一行三个整数 $n,m,k$，含义见上文。 第二行共 $n$ 个数，第 $i$ 个为 $a_i$，表示物品的大小。 ### 输出格式 一行一个数，表示最多可以放入多少个物品。 ### 说明/提示 #### 样例解释 - 在第一组样例中，可以将后 $4$ 个放入盒子。 - 在第二组样例中仅有一个盒子，故只能放入最后一个。 - 在第三组样例中有 $3$ 个大小为 $3$ 的盒子，每个盒子正好装满。 #### 数据规模与约定 保证 $1\le n,m\le2\times 10^5$，$1\le k\le10^9$，$1\le a_i\le k$。

Maksim has $ n $ objects and $ m $ boxes, each box has size exactly $ k $ . Objects are numbered from $ 1 $ to $ n $ in order from left to right, the size of the $ i $ -th object is $ a_i $ . 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 $ i $ -th object fits in the current box (the remaining size of the box is greater than or equal to $ a_i $ ), he puts it in the box, and the remaining size of the box decreases by $ a_i $ . 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).

The first line of the input contains three integers $ n $ , $ m $ , $ k $ ( $ 1 \le n, m \le 2 \cdot 10^5 $ , $ 1 \le k \le 10^9 $ ) — the number of objects, the number of boxes and the size of each box. The second line of the input contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 1 \le a_i \le k $ ), where $ a_i $ is the size of the $ i $ -th object.

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

5 2 6
5 2 1 4 2

4

5 1 4
4 2 3 4 1

1

5 3 3
1 2 3 1 1

5

In the first example Maksim can pack only $ 4 $ objects. Firstly, he tries to pack all the $ 5 $ objects. Distribution of objects will be $ [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] $ . So the answer is $ 4 $ . 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] $ ), but he can pack the last object ( $ [1] $ ). In the third example Maksim can pack all the objects he has. The distribution will be $ [1, 2], [3], [1, 1] $ .