How can I check if multiplying two numbers in Java will cause an overflow?

I want to handle the special case where multiplying two numbers together causes an overflow. The code looks something like this:

int a = 20;
long b = 30;

// if a or b are big enough, this result will silently overflow
long c = a * b;

That's a simplified version. In the real program a and b are sourced elsewhere at runtime. What I want to achieve is something like this:

long c;
if (a * b will overflow) {
    c = Long.MAX_VALUE;
} else {
    c = a * b;
}

How do you suggest I best code this?

Update: a and b are always non-negative in my scenario.