Allyn is playing a new strategy game called "Accumulator Apex". In this game, Allyn is given the initial value of an integer $$$x$$$, referred to as the accumulator, and $$$k$$$ lists of integers. Allyn can make multiple turns. On each turn, Allyn can withdraw the leftmost element from any non-empty list and add it to the accumulator $$$x$$$ if the resulting $$$x$$$ is non-negative. Allyn can end the game at any moment. The goal of the game is to get the largest possible value of the accumulator $$$x$$$. Please help Allyn find the largest possible value of the accumulator $$$x$$$ they can get in this game.
The first line of the input contains two integers $$$x$$$ and $$$k$$$ ($$$0 \leq x \leq 10^9, 1 \leq k \leq 10^5$$$) — the initial value of the accumulator $$$x$$$ and the number of lists. The next $$$k$$$ lines contain the description of lists: an integer $$$l_i$$$ ($$$l_i \ge 1$$$) followed on the same line by $$$l_i$$$ elements of the list in the order from left to right. Each element of lists does not exceed $$$10^9$$$ by the absolute value, and the total size of all lists does not exceed $$$10^5$$$.
The sole line of the output should contain the largest value of the accumulator $$$x$$$ Allyn can get.
1 32 -1 22 -2 32 -3 4
4
1 23 -1 -1 44 1 -3 -4 8
4
In the first input, we start with $$$x = 1$$$. Then, we can take the first integer from the first list and get $$$x = 0$$$ — adding the next integer $$$2$$$ from the first list we get $$$x = 2$$$. After that, we can add the integers from the second list and obtain $$$x = 3$$$. Finally, we can add the integers from the third list and obtain $$$x = 4$$$.
In the second input, we can add the first integer from the second list and get $$$x = 2$$$. Then, by adding the elements from the first list, we get $$$x = 4$$$. We cannot add more integers to increase $$$x$$$.