What is wrong with the conditional statement if?

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I want to make a function that generates randomly a matrix which

1. Has $m$-different rows and $k$ columns
2. The entries in each row are in a certain range $n$ and they do not repeat
3. The sum of entries in each row is an even number

I have written the following code:

 def generate(n,m,k):
    if (m>binomial(n,k) or k>n):
        print("error")
    else:
        a=matrix(m,k,0)
        a[0]=sample(xrange(0,n),k)

        j=1
        while j<m:
            r=sample(xrange(0,n),k)    #candidate-row
            c=sum(r)                   #sum of entries of the candidate- row

            count=0
            for i in xrange(0,j-1): #here we check if the candidate-row appeared before in the matrix
                if (r==a[i]):
                    count=count+1

            if (count==0 and mod(c,2)==0):    #we take r if it did not appear before 
                a[j]=r                        #and the sum of entries is even
                j=j+1

        print(a.str())

When I call the function I notice that the rows actually are repeating and the sum in each row is not an even number and I can't understand why. Any suggestion is appreciated!