10156_Stamps

Given a set of N stamp values (e.g., {1 cent, 3 cents}) and an upper limit K to the number of stamps that can fit on an envelope, calculate the largest unbroken list of postages from 1 cent to M cents that can be created.

For example, consider stamps whose values are limited to 1 cent and 3 cents; you can use at most 5 stamps. It's easy to see how to assemble postage of 1 through 5 cents (just use that many 1 cent stamps), and successive values aren't much harder:

6 = 3 + 3
7 = 3 + 3 + 1
8 = 3 + 3 + 1 + 1
9 = 3 + 3 + 3
10 = 3 + 3 + 3 + 1
11 = 3 + 3 + 3 + 1 + 1
12 = 3 + 3 + 3 + 3
13 = 3 + 3 + 3 + 3 + 1

However, there is no way to make 14 cents of postage with 5 or fewer stamps of value 1 and 3 cents. Thus, for this set of two stamp values and a limit of K=5, the answer is M=13.

The most difficult test case for this problem has a time limit of 3 seconds.

Line 1:            Two integers K and N. K (1 ≤ K ≤ 200) is the total number of stamps that can be used. N (1 ≤ N ≤ 50) is the number of stamp values.

Lines 2..end:   N integers, 15 per line, listing all of the N stamp values, each of which will be at most 10000.

One line :  One integer, the number of contiguous postage values starting at 1 cent that can be formed using no more than K stamps from the set.

5 2
1 3

13