We'll define *S*(*n*) for positive integer *n* as follows: the number of the *n*'s digits in the decimal base. For example, *S*(893) = 3, *S*(114514) = 6.

You want to make a consecutive integer sequence starting from number *m* (*m*, *m* + 1, ...). But you need to pay *S*(*n*)·*k* to add the number *n* to the sequence.

You can spend a cost up to *w*, and you want to make the sequence as long as possible. Write a program that tells sequence's maximum length.
The first line contains three integers *w* (1 ≤ *w* ≤ 10<sup class="upper-index">16</sup>), *m* (1 ≤ *m* ≤ 10<sup class="upper-index">16</sup>), *k* (1 ≤ *k* ≤ 10<sup class="upper-index">9</sup>).

Please, do not write the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.
def cnt(x, y):
  return y-x

w, m, k = map(int, input().split())
p, d, res = 1, 0, 0
while p <= m:
  p *= 10
  d += 1
while cnt(m, p)*d*k <= w:
  w -= cnt(m, p)*d*k
  res += cnt(m, p)
  m = p
  p *= 10
  d += 1
lo, hi = m, p
while hi-lo > 1:
  mid = (lo+hi)//2
  if (cnt(m, mid)*d*k <= w): lo = mid
  else: hi = mid
res += cnt(m, lo)

print(res)
