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hihoCoder

给定一个数 x,设它十进制展从高位到低位上的数位依次是 a0, a1, ..., an - 1,定义交错和函数:

f(x) = a0 - a1 + a2 - ... + ( - 1)n - 1an - 1

例如:

f(3214567) = 3 - 2 + 1 - 4 + 5 - 6 + 7 = 4

给定 l, r, k,求在 [l, r] 区间中,所有 f(x) = kx 的和,即:

1405402477702.png

输入

输入数据仅一行包含三个整数,l, r, k(0 ≤ l ≤ r ≤ 1018, |k| ≤ 100)。

输出

输出一行一个整数表示结果,考虑到答案可能很大,输出结果模 109 + 7

提示

对于样例 ,满足条件的数有 110 和 121,所以结果是 231 = 110 + 121。


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