P5691 [NOI2001] Number of Solutions of an Equation

Given an $n$-variable higher-degree equation: $$\sum\limits_{i=1}^n k_ix_i^{p_i} = 0$$ where $x_1, x_2, \dots, x_n$ are the unknowns, $k_1, k_2, \dots, k_n$ are the coefficients, and $p_1, p_2, \dots, p_n$ are the exponents. All numbers in the equation are integers. Assume the unknowns satisfy $x_i \in [1,m] \space ( i \in [1,n])$. Find the number of integer solutions to this equation.

The first line contains a positive integer $n$, the number of unknowns. The second line contains a positive integer $m$. The next $n$ lines each contain two integers $k_i, p_i$.

Output one line with one integer, the number of solutions of the equation.

**【Constraints】** For $100\%$ of the testdata, $1\le n \le 6$, $1\le m \le 150$, and $$\sum\limits_{i=1}^n |k_im^{p_i}| < 2^{31}$$ The answer does not exceed $2^{31}-1$, and $p_i \in \mathbb N^*\cap[0,2^{31})$. Translated by ChatGPT 5