Hello, codeforces!

As you can observe from my rank, I am quite a codeforces newbie. I spend all my days on the sacred romanian OJ, Infoarena( https://www.infoarena.ro/ ), and, more recently, Kilonova( https://kilonova.ro/ ). Altough the blue color is dominating my profile and I should not be taken seriously for such heresy, I want to share with the good people of codeforces an interesting problem. Please do not bully me, despite my little experience. I would be honored to hear your opinion.

This is the problem: You are given a string S of digits separated by the following operators: +, , -, /, ^(pow), $(xor), &, |, (, ). Parentheses have biggest priority, then: '^'(pow) > '/' > '' > '+' > '-' > '&' > '|' > '$'(xor).

The task is to find out in how many ways modulo 10^9 + 7 you can rearrange the characters of the string such that the result is a given X(X < 10).

|S| <= 2 * 10 ^ 5. Time limit: 0.01 seconds Memory limit: common sense

I know how to solve this problem, but my solution is, as we call it in Romania, a very big "tractor" (translation for truck). I am very curious for what you come up with.

Best wishes, Geanina.