First, let's understand the criterion for being able to reach point $$$L$$$ from point $$$0$$$ using a set of jump lengths $$$x_1, x_2, \dots, x_n$$$. From the extended Euclidean algorithm, it is not difficult to understand that from point $$$0$$$, we can reach point $$$g = \gcd(x_1, x_2, \dots, x_n$$$) using a linear combination of jumps. Obviously, after that, we can visit all coordinates of the form $$$g \cdot k$$$, where $$$k \in \mathbb{Z}$$$.

Next, we will show that the points described above are all the points that can be visited with such a set of $$$x$$$ values. Indeed, each of $$$x_1, x_2, \dots, x_n$$$ is divisible by $$$g$$$, thus the coordinate after a jump will always be a multiple of $$$g$$$.

After that, we want point $$$L$$$ to be equal to $$$g \cdot k$$$ for some integer $$$k$$$. Thus, the necessary and sufficient condition for the set of $$$x$$$ values is: $$$L \mathrel{\vdots} \gcd(x_1, x_2, \dots, x_n)$$$.

Then the problem reduces to finding a set of $$$x$$$ values with the minimum cost such that its $$$\gcd$$$ divides $$$L$$$. Therefore, from the current set, we are only interested in its current $$$\gcd$$$ and cost. Let's set up a dynamic programming approach:

$$$d p_{i, z}$$$ — the minimum cost of a set formed only from the first $$$i$$$ abilities that has $$$\gcd = z$$$. We will understand how to recalculate such a DP: if the current ability has parameters $$$x_i$$$, $$$c_i$$$, then the recalculation from the previous layer will be as follows:

$$$$$$dp_{i, \gcd(w, x_i)} = \min(dp_{i, \gcd(w, x_i)}, dp_{i-1, w} + c_i), \,\,\,\,\,\,\,\,\,\,\,\,\,\,0 \leq w \leq L$$$$$$

Thus, the DP works in $$$\mathcal{O}(n \cdot L \cdot \log C)$$$. How to find the answer? We need to look at all DP values of the form $$$dp_{n, d}$$$, where $$$d$$$ divides $$$|L|$$$.