Yogurt factory

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시간 제한1초메모리 제한1024 MB

요약

주마다 단위 생산 비용과 배송 수요가 주어지고, 한 단위를 한 주 보관하는 데 S센트가 든다. N주 동안의 최소 총비용을 구한다.

난이도: 보통10점 중 4점
유형: 그리디, 구현, 배열, 동적 계획법
정답자: 아직 제출이 없습니다

문제

The cows have purchased a yogurt factory that makes world-famous Yucky Yogurt. Over the next N (1 ≤ N ≤ 10,000) weeks, the price of milk and labor will fluctuate weekly such that it will cost the company C_i (1 ≤ C_i ≤ 5,000) cents to produce one unit of yogurt in week i. Yucky's factory, being well-designed, can produce arbitrarily many units of yogurt each week.

Yucky Yogurt owns a warehouse that can store unused yogurt at a constant fee of S (1 ≤ S ≤ 100) cents per unit of yogurt per week. Fortuitously, yogurt does not spoil. Yucky Yogurt's warehouse is enormous, so it can hold arbitrarily many units of yogurt.

Yucky wants to find a way to make weekly deliveries of Y_i (0 ≤ Y_i ≤ 10,000) units of yogurt to its clientele (Y_i is the delivery quantity in week i). Help Yucky minimize its costs over the entire N-week period. Yogurt produced in week i, as well as any yogurt already in storage, can be used to meet Yucky's demand for that week.

입력

Line 1: Two space-separated integers, N and S.
Lines 2..N+1: Line i+1 contains two space-separated integers: C_i and Y_i.

출력

Line 1: Line 1 contains a single integer: the minimum total cost to satisfy the yogurt schedule. Note that the total might be too large for a 32-bit integer.

힌트

In week 1, produce 200 units of yogurt and deliver all of it. In week 2, produce 700 units: deliver 400 units while storing 300 units. In week 3, deliver the 300 units that were stored. In week 4, produce and deliver 500 units.

예제1

예제 1
입력
```
4 5
88 200
89 400
97 300
91 500
```
예상 출력
```
126900
```