Farmer John suffered a terrible loss when giant Australian cockroaches ate the entirety of his hay inventory, leaving him with nothing to feed the cows. He hitched up his wagon with capacity $C$ $(1 \le C \le 50,000)$ cubic units and sauntered over to Farmer Don's to get some hay before the cows miss a meal.
Farmer Don had a wide variety of $H$ $(1 \le H \le 5,000)$ hay bales for sale, each with its own volume $(1 \le V_{i} \le C)$. Bales of hay, you know, are somewhat flexible and can be jammed into the oddest of spaces in a wagon.
FJ carefully evaluates the volumes so that he can figure out the largest amount of hay he can purchase for his cows.
Given the volume constraint and a list of bales to buy, what is the greatest volume of hay FJ can purchase? He can't purchase partial bales, of course. Each input line (after the first) lists a single bale FJ can buy.
Input
- Line 1: Two space-separated integers: $C$ and $H$
- Lines $2,\ldots,H+1$: Each line describes the volume of a single bale: $V_{i}$
Output
- Line 1: A single integer which is the greatest volume of hay FJ can purchase given the list of bales for sale and constraints.
Examples
Input 1
7 3 2 6 5
Output 1
7
The wagon holds 7 volumetric units; three bales are offered for sale with volumes of 2, 6, and 5 units, respectively.
Buying the two smaller bales fills the wagon.
Problem credits: Rob Kolstad (traditional), 2008