bug in subset sum algorithm

[usercat123]

Given an array of integers and a value k, return True if there exists a subset of elements of the array that sums up to k.
This is my algorithm. Initially, the line that I commented was included and the result was that the algorithm outputted True when the answer should have been False. Without the line it seems to work fine. I do not understand why there is a difference in output, can somebody explain?

def solve(arr,items,sum,dp):
    if sum - arr[items] >= 0:
        dp[items][sum] = max(dp[items-1][sum],dp[items-1][sum-arr[items]])
    else:
        dp[items][sum] = dp[items-1][sum]

def driver(arr,k):
    dp = [[False for j in range(k+1)] for i in range(len(arr))]
    for i in range(len(arr)):
        dp[i][0] = True
        #why does this not work if the line below is executed?
        #dp[i][arr[i]] = True
    for i in range(len(arr)):
        for j in range(k+1):
            solve(arr,i,j,dp)
    return dp[len(arr)-1][k]