Find minimum $x$ such that for all $y\geq x$, a combination of cents exists that adds upto $y$. ($p_1$ to $p_n$ denominations of cents available).

Question

Given cents of value $p_1,p_2,p_3,\cdots ,p_n$. Aim is to find minimum value of $x$ such that for all $y>=x$, there exists a combination of given cents denomination that adds upto $y$. All $p_i$'s are positive integers.

For $n=2$ and numbers of the form $k,k+1,k(k-1)$ seem to work good but can we prove if it is the minimum possible, i tried using induction but got stuck at the inductive step.