Counting problem

Supose that n has L digits, we used $d_0, d_1, d_2, \ldots, d_{L-1}$ to indicate every digit of n from least significant digit to most significant one.
$f(n, k) = \sum\limits_{i=0}^{L-1}d_i^k$, for example $f(305, 2) = 5^2 + 3^2 + 0^2 = 34$
We are curious about that for each x ranged from a to b($a \leq b$), how many integers make $S=f(x, k)$ (here S is a constant) true.

Multi test cases (about 100), every case gives four integers a, b, k, S in a single line.
Please process to the end of file.

[Technical Specification]
$1 \leq a \leq b \leq 999999999$
$1 \leq k \leq 15$
$1 \leq S \leq 10^{16}$

For each case，output a number in a single line indicates how many x ranged from a to b makes $S=f(x, k)$ true.

1 1 1 1
1 10 2 1

1
2

BestCoder Round #15