Binary index tree optimization

I have written code for a binary index tree. My problem is that there are many functions based on the binary index tree the function stores the sum of element within a given range of binary index tree. My task is to compute the sum of all the functions with provide range.

This example will clarify:

My array elements: A = 1 2 3 4 5

The function \$f(x,y)\$ is the sum of all elements of array between index \$x\$ and \$y\$ (inclusive)

1. \$f(1,3) = 6\$
2. \$f(2,5) = 14\$
3. \$f(4,5) = 9\$
4. \$f(3,5) = 12\$
5. \$f(1,2) = 3\$

For a given query of the form sum(a,b), I have to compute the sum of all the function from a to b.

sum(1,4) is the sum of the function from 1 to 4:

\$f(1,3) + f(2,5) + f(4,5) + f(3,5) = 6+14+9+12 = 41\$

The above data structure must also support for updating in the array.

• update(a,b) replaces the element stored in index a of the array with b
• update(3,7) will cause my new array to be A = 1 2 7 4 5

For any further clarification you can refer to this link.

My code is working for smaller range of input. How can I tune it to work for larger inputs?

def initupdate(x, y, n, lst):
    while x <= n:
        lst[x] += y
        x += (x & -x)

def update(x, y, n, lst):
    a = lst[x]
    initupdate(x, -a, n, lst)
    initupdate(x, y, n, lst)

def sumk(k, lst):
    res = 0
    while k:    
        res += lst[k]
        k -= (k & -k)
    return res

def sumfunc(k, nfunc, lst):
        res = 0
        a, b = nfunc[k]
        res += sumk(b, lst)
        res -= sumk(a - 1, lst)
        return res

def sumfuncxy(x,y, nfunc, lst):
    res=0
    for k in range(x,y+1):
        res+=sumfunc(k,nfunc,lst)
    return res

n = int(input())
array = [0] + list(map(int, input().split()))
number = [ 0 for i in range(n + 1)]

for i in range(1, n + 1):
    initupdate(i, array[i], n, number)

nfunction = [[0, 0] for i in range(n + 1)]

for i in range(1, n + 1):
    lst = input().split()
    lst = list(map(int, lst))
    nfunction[i] = lst

q = int(input())

for i in range(q):
    lst = list(map(int, input().split()))
    if lst[0] == 1:
        'update'
        update(lst[1], lst[2], n, number)
    else:
        print(sumfuncxy(lst[1], lst[2], nfunction, number))

I know my naming of the variable is poor.

1. Is the choice of data structure (binary index tree) good for the problem?
2. Have I properly modularized my code?
3. Are there any vulnerability in my code?
4. Are there any further suggestions for cleaning the code?