Imagine on your table, you have a paper in the shape of an isosceles right triangle ABC, where AB are the endpoints of the hypotenuse. An operation is defined by the following folds. You join A to C and B to C forming a square. You then join the two diagonally opposite vertices of the newly formed square (previously, the midpoints of AC and BC respectively), creating a smaller right angled triangle.

If you unfold the paper completely after one operation, you may notice that the crease made is inwards. We define this as a valley. Multiple operations may also lead to the formation of an outwards crease, which is defined as a mountain.

Let $M$ be the total length of all mountains and $V$ be the total length of all valleys after $319587138362$ such operations. Consider the simple reduced fraction $\frac{p}{q}$ to be the ratio of $M$ and $V$.

Return $3\cdot p\ +\ 2\cdot q\ $ modulo $1,000,000,007$.