# input: a[0..N) array of integers, N>=0, and S
#
# output: is there a subarray of a[0..N) whose sum is S?
#
# exponential (in N ans S) naive solution

def ss_naive(a,S):
  return ss_aux(a,len(a),S)

def ss_aux(a,n,s):
  ans = None
  if n==0: ans = (s==0)
  else:
    if a[n-1]>s: ans = ss_aux(a,n-1,s)
    else: ans = max(ss_aux(a,n-1,s),ss_aux(a,n-1,s-a[n-1]))