// here they're using a One-based indexing approach

void add(int idx, int val) { // basically add val to the i-th element
    // notice that they use idx for a range like [0, N-1], hence the "++idx"
    for (++idx; idx < n; idx += idx & -idx) 
        bit[idx] += val;
}

void range_add(int l, int r, int val) { // add val to element to [l, r]
    add(l, val);
    add(r + 1, -val);
}

int point_query(int idx) {
    int ret = 0;
    for (++idx; idx > 0; idx -= idx & -idx)
        ret += bit[idx];
    return ret;
}

// In this code they're using 2 BIT, B1 and B2

def add(b, idx, x):
    while idx <= N:
        b[idx] += x
        idx += idx & -idx

def range_add(l,r,x):
    add(B1, l, x)
    add(B1, r+1, -x)
    add(B2, l, x*(l-1))
    add(B2, r+1, -x*r)

def sum(b, idx):
    total = 0
    while idx > 0:
        total += b[idx]
        idx -= idx & -idx
    return total

def prefix_sum(idx):
    return sum(B1, idx)*idx -  sum(B2, idx)

def range_sum(l, r):
    return prefix_sum(r) - prefix_sum(l-1)