Centipede legs

When Phil was a boy he kept a centipede. Centipedes have many legs. Phil's centipede had $n$ legs in total: some of them were left legs and the rest were right legs. Every day the centipede used some of its legs, and it always used at least one left leg and at least one right leg.

Each day Phil wrote down in his notebook how many left legs and how many right legs the centipede used that day.

Phil now wants to recover from his notes how many left legs and how many right legs his centipede had. Phil was not accurate, so some notes may be wrong. A note $l_i, r_i$ is correct if the centipede had at least $l_i$ left legs and at least $r_i$ right legs.

Choose a number of left legs and a number of right legs that makes the number of correct notes as large as possible. Each of the two counts is at least 1, and together they add up to $n$.

The input contains several test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$).

The first line of each test case contains the total number of centipede legs $n$ ($2 \le n \le 10^9$). The next line contains the number of Phil's notes $m$ ($1 \le m \le 10^5$).

Each of the following $m$ lines contains two integers $l_i$ and $r_i$, the number of left legs and the number of right legs the centipede used on day $i$ according to Phil's notes ($1 \le l_i, r_i \le n$).

The total number of notes over all test cases in one input does not exceed $10^5$.

For each test case print one line with two integers: the number of left legs and the number of right legs that make the number of correct notes as large as possible.

If several answers reach that maximum, print the one with the smallest number of left legs.