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

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

• $1<x_1<x_2<...<x_n<y_1<...<y_m.$

• $x_1+x_2+...+x_n<y_1+...y_m.$

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

(form inernet)

I don't have an ideal for this problems.Thanks for your help.