human
Give me a Python program to determine when Alexander gets ahead of Arthur if both guys start performing the operations at the same time given the following:
Arthur and Alexander are number busters. Today they've got a competition. 

Arthur took a group of four integers a, b, w, x (0 ≤ b < w, 0 < x < w) and Alexander took integer с. Arthur and Alexander use distinct approaches to number bustings. Alexander is just a regular guy. Each second, he subtracts one from his number. In other words, he performs the assignment: c = c - 1. Arthur is a sophisticated guy. Each second Arthur performs a complex operation, described as follows: if b ≥ x, perform the assignment b = b - x, if b < x, then perform two consecutive assignments a = a - 1.
b = w - (x - b).

You've got numbers a, b, w, x, c. Determine when Alexander gets ahead of Arthur if both guys start performing the operations at the same time. Assume that Alexander got ahead of Arthur if c ≤ a.

Input

The first line contains integers a, b, w, x, c (1 ≤ a ≤ 2·109, 1 ≤ w ≤ 1000, 0 ≤ b < w, 0 < x < w, 1 ≤ c ≤ 2·109).

Output

Print a single integer — the minimum time in seconds Alexander needs to get ahead of Arthur. You can prove that the described situation always occurs within the problem's limits.

Examples

Input

4 2 3 1 6

Output

2

Input

4 2 3 1 7

Output

4

Input

1 2 3 2 6

Output

13

Input

1 1 2 1 1

Output

0
Using python can you solve the prior task?
assistant
#Here is Python program to determine when Alexander gets ahead of Arthur if both guys start performing the operations at the same time.

def gao(b, w, x):
    r = []
    pos = dict()
    idx = None
    while True:
        if not pos.get(b) is None:
            idx = pos.get(b)
            break
        pos[b] = len(r)
        if b >= x:
            r.append((b, False))
            b -= x
        else:
            r.append((b, True))
            b += w - x
    return r[:idx], r[idx:]

def work(a, c, pc, rc):

    def ceil(x, y):
        return x //y + 1 if x % y != 0 else x // y

    steps = 0
    # Begin
    if c <= a:
        print steps
        return
    for t in pc:
        steps += 1
        c -= 1
        if t[1]:
            a -= 1
        if c <= a:
            print steps
            return
    # Loop
    d = 0
    for t in rc:
        if not t[1]:
            d += 1
    nb = ceil(c - a, d)
    steps += (nb - 1) * len(rc)
    a -= (nb - 1) * (len(rc) - d)
    c -= (nb - 1) * len(rc)
    for t in rc:
        steps += 1
        c -= 1
        if t[1]:
            a -= 1
        if c <= a:
            print steps
            return

if __name__ == '__main__':
    a, b, w, x, c = [int(p) for p in raw_input().split()]
    pc, rc = gao(b, w, x)
    work(a, c, pc, rc)