For two positive integer sequences $x_1,x_2,\ldots,x_n$ and $y_1,y_2,\ldots,y_m$ satisfying

• $x_i\neq x_j\quad \text{and}\quad y_i\neq y_j\quad \forall i,j, i \ne j$

• $1<x_1<x_2<\cdots<x_n<y_1<\cdots<y_m.$

• $x_1+x_2+\cdots+x_n>y_1+\cdots+y_m.$

Prove that: $x_1\cdot x_2\cdots x_n>y_1\cdot y_2\cdots y_m$.

(from internet)

I don't have an idea for this problem. Thanks for your help.