102032: [AtCoder]ABC203 C - Friends and Travel costs

Problem Statement

There are $10^{100}+1$ villages, labeled with numbers $0$, $1$, $\ldots$, $10^{100}$.
For every integer $i$ between $0$ and $10^{100}-1$ (inclusive), you can pay $1$ yen (the currency) in Village $i$ to get to Village $(i + 1)$. There is no other way to travel between villages.

Taro has $K$ yen and is in Village $0$ now. He will try to get to a village labeled with as large a number as possible.
He has $N$ friends. The $i$-th friend, who is in Village $A_i$, will give Taro $B_i$ yen when he reaches Village $A_i$.
Find the number with which the last village he will reach is labeled.

Constraints

• $1 \leq N \leq 2\times 10^5$
• $1 \leq K \leq 10^9$
• $1 \leq A_i \leq 10^{18}$
• $1 \leq B_i \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$
$A_1$ $B_1$
$:$
$A_N$ $B_N$

Output

Print the answer.

Sample Input 1

2 3
2 1
5 10

Sample Output 1

4

Takahashi will travel as follows:

• Go from Village $0$ to Village $1$, for $1$ yen. Now he has $2$ yen.
• Go from Village $1$ to Village $2$, for $1$ yen. Now he has $1$ yen.
• Get $1$ yen from the $1$-st friend in Village $2$. Now he has $2$ yen.
• Go from Village $2$ to Village $3$, for $1$ yen. Now he has $1$ yen.
• Go from Village $3$ to Village $4$, for $1$ yen. Now he has $0$ yen, and he has no friends in this village, so his journey ends here.

Thus, we should print $4$.

Sample Input 2

5 1000000000
1 1000000000
2 1000000000
3 1000000000
4 1000000000
5 1000000000

Sample Output 2

6000000000

Note that the answer may not fit into a $32$-bit integer.

Sample Input 3

3 2
5 5
2 1
2 2

Sample Output 3

10

He may have multiple friends in the same village.