6214번 - Problem Solving 다국어

문제

In easier times, Farmer John's cows had no problems. These days, though, they have problems, lots of problems; they have P (1 <= P <= 300) problems, to be exact. They have quit providing milk and have taken regular jobs like all other good citizens. In fact, on a normal month they make M (1 <= M <= 1000) money.

Their problems, however, are so complex they must hire consultants to solve them. Consultants are not free, but they are competent: consultants can solve any problem in a single month. Each consultant demands two payments: one in advance (1 <= payment <= M) to be paid at the start of the month problem-solving is commenced and one more payment at the start of the month after the problem is solved (1 <= payment <= M). Thus, each month the cows can spend the money earned during the previous month to pay for consultants. Cows are spendthrifts: they can never save any money from month-to-month; money not used is wasted on cow candy.

Since the problems to be solved depend on each other, they must be solved mostly in order. For example, problem 3 must be solved before problem 4 or during the same month as problem 4.

Determine the number of months it takes to solve all of the cows' problems and pay for the solutions.

입력

• Line 1: Two space-separated integers: M and P.
• Lines 2..P+1: Line i+1 describes problem i with two space-separated integers: B_i and A_i. B_i is the payment to the consult BEFORE the problem is solved; A_i is the payment to the consult AFTER the problem is solved.

출력

• Line 1: The number of months it takes to solve and pay for all the cows' problems.

제한

힌트

+------+------+--------+---------+---------+--------+
| | Avail | Probs | Before | After | Candy |
|Month | Money | Solved | Payment | Payment | Money |
+------+-------+--------+---------+---------+--------+
| 1 | 0 | -none- | 0 | 0 | 0 |
| 2 | 100 | 1, 2 | 40+60 | 0 | 0 |
| 3 | 100 | 3, 4 | 30+30 | 20+20 | 0 |
| 4 | 100 | -none- | 0 | 50+50 | 0 |
| 5 | 100 | 5 | 40 | 0 | 60 |
| 6 | 100 | -none- | 0 | 40 | 60 | 
+------+-------+--------+---------+---------+--------+