How to reduce from subset-sum problem?
Suppose that you have an instance of SUBSET SUM:

$0 \leq x_1, x_2, ..., x_n$ and an integer $0 \leq t$

You must find $b_i \in \{0,1\}$ such that $b_1*x_1+b_2*x_2+...+b_n*x_n = t$

Which is equivalent to:
$b_1*x_1+b_2*x_2+...+b_n*x_n \geq t$ AND $b_1*x_1+b_2*x_2+...+b_n*x_n \leq t$

$b_1*x_1+b_2*x_2+...+b_n*x_n &gt; t-1$ AND $b_1*x_1+b_2*x_2+...+b_n*x_n &lt; t+1$ 

pick $P=t-1$, $T=t+1$, $M = \{ (x1,x1),....,(x_n,x_n)\}$