How many non-decreasing functions?

How many non-decreasing functions exist which map $\{1, 2, \dots, n\} \to \{1, 2, \dots, m\}$?

i.e

How many ordered pairs $(x_1, x_2, \dots, x_n)$ exist such that

$x_i \le x_{i+1}$ and $1 \le x_i \le m$ for all $i$?

[Solution]