题目202：激光束

欧拉计划

Laserbeam

Three mirrors are arranged in the shape of an equilateral triangle, with their reflective surfaces pointing inwards. There is an infinitesimal gap at each vertex of the triangle through which a laser beam may pass.

Label the vertices A, B and C. There are 2 ways in which a laser beam may enter vertex C, bounce off 11 surfaces, then exit through the same vertex: one way is shown below; the other is the reverse of that.

There are 80840 ways in which a laser beam may enter vertex C, bounce off 1000001 surfaces, then exit through the same vertex.

In how many ways can a laser beam enter at vertex C, bounce off 12017639147 surfaces, then exit through the same vertex?

题目：

三面镜子摆出了等边三角形的形状，它们的反射面都向里。每个顶点都有一个极小的缺口，光线可以从该缺口中照射进来。

三个顶点分别标记为 A、B、C。我们知道有两种光线的照射方式，可以从 C 点进入，在镜面发生 11 次反射，然后又从同一点出去：其中一种方式如下图所示，而另一种则是前一种的逆过程。

我们还知道有 80840 种光线照射方式，从 C 点进入，发生 1000001 次表面反射，然后从同一点出去。

请问，从 C 点进入，经过 12017639147 次反射，再从 C 点出去的光线照射方式有多少种？