## The Problem

Time Limit: 5000 MS Memory Limit: 65536 K

Bessie, always in need of an income, has decided to leverage her
dairy skills by taking a part-time job at the local Dairy Queen
restaurant. She is running a special cash register (since she has
hooves instead of fingers and thus requires special accommodation).
Her job is making change for customers as they make a purchase.
As she was counting out 83 cents in change, she wondered: "How many
ways can I count out 83 cents? I can use three quarters and eight
pennies, seven dimes and three pennies, 83 pennies... there must
be a zillion ways!"
How many different ways can one make change for N (1 <= N <= 300)
cents using coins from a set of C (1 <= C <= 8) coins of supplied
values C_i (1 <= C_i <= 200)? "Different" means differing counts
of coins.
Thus, 8 cents can be made, in American currency, with 1 five-cent
piece + 3 one-cent pieces and also with 8 one-cent pieces. Using 3
one-cent pieces + 1 five-cent piece is the same as 1 five-cent piece
+ 3 one-cent pieces, so one can create eight cents in just two
different ways. Note that some coin systems are poor at making
change and result in an answer of '0'.
Coin values in the input file are listed in descending order from
largest to smallest. All coin values will be distinct.
HINT: Consider recursion as a solution technique.
## INPUT FORMAT:

* Line 1: Two space-separated integers: N and C
* Lines 2..C+1: Line i+1 contains a single integer: C_i
## SAMPLE INPUT:

83 5

50

25

10

5

1

## INPUT DETAILS:

Eight-three cents; standard American coins with values 50, 25, 10, 5, and 1
## OUTPUT FORMAT:

* Line 1: A single line with a single integer that is the number of
ways to create N cents of change using the supplied coins. The
answer is guaranteed to fit into a signed 32-bit integer.
## SAMPLE OUTPUT:

159

## OUTPUT DETAILS:

Here are 15 of the 159 ways of making 83 cents:
0 x 50 0 x 25 0 x 10 0 x 5 83 x 1

0 x 50 0 x 25 0 x 10 1 x 5 78 x 1

0 x 50 0 x 25 0 x 10 2 x 5 73 x 1

0 x 50 0 x 25 0 x 10 3 x 5 68 x 1

0 x 50 0 x 25 0 x 10 4 x 5 63 x 1

0 x 50 0 x 25 0 x 10 5 x 5 58 x 1

0 x 50 0 x 25 0 x 10 6 x 5 53 x 1

0 x 50 0 x 25 0 x 10 7 x 5 48 x 1

0 x 50 0 x 25 0 x 10 8 x 5 43 x 1

0 x 50 0 x 25 0 x 10 9 x 5 38 x 1

0 x 50 0 x 25 0 x 10 10 x 5 33 x 1

0 x 50 0 x 25 0 x 10 11 x 5 28 x 1

0 x 50 0 x 25 0 x 10 12 x 5 23 x 1

0 x 50 0 x 25 0 x 10 13 x 5 18 x 1

0 x 50 0 x 25 0 x 10 14 x 5 13 x 1