hello codeforces,

I have come here to ask help to dp experts. I will highly appreciate it if you can help solve this dilemma. I have been struggling with this for a while now.

The problem can be found here.

http://mirror.codeforces.com/contest/69/problem/D

I have stepped through the logic of my DP formulation and i dont seem to spot the fallacy. So, can you please point out the point where my logic fails. I will highly appreciate it. Thanks for your time. I have commented out parts of my code for legibility.

The test case that fails is the following

-100 -100 10 200
0 1
1 0
1 1
31 41
3 4
5 2
1 2
3 3
9 8
10 2

Code starts below

import math


vectors = []

line_parts = raw_input().split()
x = int(line_parts[0])
y = int(line_parts[1])
n = int(line_parts[2])
d = int(line_parts[3])

for i in range(n):
  l = raw_input().split()
  vectors.append((int(l[0]), int(l[1])))

mp = {}


def canWin(x, y, t, fs, ss):

  if math.sqrt(math.pow(x, 2) + math.pow(y, 2)) > float(d):
    return False

  if (x, y, t) in mp:
    return mp[(x, y, t)]  
    
  result = True 
    
  if t == False and ss == False:  #if Dasha turn and if dasha hasnt swapped then can swap 1 time
    for v in vectors:
      result = result and (not (canWin(x + v[0], y + v[1], not t, fs, ss)))
    result = result and (not canWin(y, x, not t, fs, True)) #swap step
  elif t == True and fs == False: #if Anton turn and if Anton hasnt swapped then can swap 1 time
    for v in vectors:
      result = result and (not (canWin(x + v[0], y + v[1], not t, fs, ss)))
    result = result and (not canWin(y, x, not t, True, ss)) #swap step
  else: #since both has swapped 1 time now cannot swap further
    for v in vectors:
      result = result and (not (canWin(x + v[0], y + v[1], not t, fs, ss)))

      
  mp[(x, y, t)] = result
  
  return result
      

result = False

for v in vectors:
  result = result or canWin(x + v[0], y + v[1], False, False, False)      
      
if result == True:
  print "Anton"
else:
  print "Dasha"