Some Impact

Consider the infinite $x$ axis. There are $N$ impacts on this X-axis at integral points ($X_1$,$X_2$,....$X_N$) (all distinct) . An impact at a point $X$i propagates such that at a point $X$0, the effect of the impact is $K^{|X_i - X_0|}$. Given the point $X_0$, $N$ and $K$. Assume the total impact on $X_0$ is $M$, find if it is possible to do so. Note: You are not required to find the set X Fo