# Let X be multivariate hypergeometrically distributed with s
# categories having assigned values x_1,...x_s having f_1,...f_s
# instances in the urn.  m is the sum of all the f_i.

# Let Y be the sum of of n observations from X. Y is discrete random
# variable of s' values y_1,...y_s' with frequency g_1,...g_s'.

# Y will range from n*x_0 to n*x_s, and s' is given by
# | Outer Sum from 1..n of the set { x_0,...,x_s } |

from __future__ import division
import sys
# Factorial of N
def factorial( N ):
    if N == 0:
        return 1.0
    else:
        r = 1.0
        for i in range( 2, N+1 ):
            r *= i
        return r

# Number of combinations of r items taken from n
def combinations( n, r ):
    nCr = 1
    if (r*2) > n:
        r = n-r
    for i in range( r-1, -1, -1 ):
        nCr = ( nCr * ( n - i ) ) // ( r - i )
    return nCr

# Enumerate probability mass pieces from the sum-of-multivariate-hypergeometrics distribution
# Y, g, s, m, n, f, x are described at the top
# i is the number of the category from X that we are processing
# prob[Y] is the probability of observing sum Y
# free is the number of observations (out of n) that remain to be used
# maxfree[i] is the maximum allowed value of free at point i
# k is the number of observations to use from category i
def enumerate_mhyper_sum( i, prob, free, maxfree, Y, g, s, m, n, f, x  ):
    if free == 0:
        if Y not in prob: prob[Y] = 0
        prob[Y] += g
    else:
        for k in range( max( 0, free-maxfree[i+1] ), min( f[i], free ) + 1 ):
            enumerate_mhyper_sum( i+1, prob, free-k, maxfree, Y+(x[i]*k), g*combinations(f[i],k), s, m, n, f, x )

# Construct the sum-of-multivariate-hypergeometrics distribution
# Return a discrete distribution such that values[i] has a frequency
# of mass[i]
def construct_mhyper_sum( x, f, n ):
    s = len(x)
    m = sum(f)
    prob = dict()
    maxfree = list( f )
    for i in range( s-2, -1, -1 ):
        maxfree[i] += maxfree[i+1]
    maxfree += [ 0 ]
    enumerate_mhyper_sum( 0, prob, n, maxfree, 0, 1, s, m, n, f, x )
    values = []
    mass = []
    for k in sorted( prob.keys() ):
        values.append( k )
        mass.append( prob[k] / combinations(m,n) )
    return ( values, mass )

n = int(sys.argv[4])
x = [ -1, 0, 1 ]
f = [ int(sys.argv[1]),int(sys.argv[2]) , int(sys.argv[3]) ]
t = int(sys.argv[5])

#print f
(values,mass) = construct_mhyper_sum( x, f, n )

#for (v,d) in zip(values,mass):
#	print v, d

#print "Probability Mass Sums to: %f" % sum(mass)
#print "Population Mean (expected sum of %d observations) is: %f" % (n, sum( v*d for (v,d) in zip(values,mass) ) )
pval = 0
#print t #debug
for num in range(len(values)):
    if t == values[num]:
        if t >= 0:
            for calc in range( num, len(values) ):
            #		print mass[calc]		#debug
                pval = pval + mass[calc]
        else:
            for calc in range( 0, num+1 ):
                pval = pval + mass[calc]
                #print mass[calc]			#debug

print "1-tailed: ", pval
print "2-tailed: ", pval*2
#from matplotlib import pylab as p
#p.plot( vals, density )
#input()