Dividing coins (uva 562) - recursive dp solution in python

I am solving this problem Dividing Coins from uva. The problem is a variation of the well known 0/1 knapsack problem. I am trying to tweak my 0/1 knapsack implementation a bit to solve this problem. I have tested my code with many test cases offline and it works fine, but when I submit my code I get a Runtime Error.

When I comment out the lines where I check if the result of a subproblem is found in the dictionary. I get Time Limit Exceeded Error.

I can’t tell exactly where the problem is. However, I feel that I am not memoizing the right thing.

May you please have a look at my code and try to help? Thank you!

def recSolve(vals, remW, allItm, idx, mem):

    if idx >= allItm or remW <= 0: # remW is the remaining amount the user could get (not exceeding total/2)
        return 0

    # check if it is in mem already
    if (remW, idx) in mem:
        return mem[(remW, idx)]
    # wight of the current item is more than the remaninig weight, skip to the next item
    if vals[idx] > remW:
        return recSolve(vals, remW, len(vals), idx+1, mem)
        # choose either picking the item or not (maximize the val)
        pickIt = recSolve(vals, remW - vals[idx], len(vals), idx+1, mem) + vals[idx]
        dontPickIt = recSolve(vals, remW, len(vals), idx+1, mem)
        res = max(pickIt, dontPickIt)
        mem[(remW, idx)] = res
        return res

def solve(vals, remW):
    mem = {}
    return recSolve(vals, remW, len(vals), 0, mem)

def takeInput():
    for i in range(int(input())):
        leng = input() # not used
        coins = input() 
        vals = [int(i) for i in coins.split(' ')] # the coins
        tot_w = sum(vals) 
        res= solve(vals, tot_w//2)  # maximizing the summation while not exceeding totalCoins/2
        print(tot_w - res - res) # getting the difference