Train Service Planning

There is a railroad in Takahashi Kingdom. The railroad consists of N sections, numbered 1, 2, ..., N, and N+1 stations, numbered 0, 1, ..., N. Section i directly connects the stations i-1 and i. A train takes exactly A_i minutes to run through section i, regardless of direction. Each of the N sections is either single-tracked over the whole length, or double-tracked over the whole length. If B_i = 1, section i is single-tracked; if B_i = 2, section i is double-tracked. Two trains running in opposite directions can cross each other on a double-tracked section, but not on a single-tracked section. Trains can also cross each other at a station.

Snuke is creating the timetable for this railroad. In this timetable, the trains on the railroad run every K minutes, as shown in the following figure. Here, bold lines represent the positions of trains running on the railroad. (See Sample 1 for clarification.)

When creating such a timetable, find the minimum sum of the amount of time required for a train to depart station 0 and reach station N, and the amount of time required for a train to depart station N and reach station 0. It can be proved that, if there exists a timetable satisfying the conditions in this problem, this minimum sum is always an integer.

Formally, the times at which trains arrive and depart must satisfy the following:

• Each train either departs station 0 and is bound for station N, or departs station N and is bound for station 0.
• Each train takes exactly A_i minutes to run through section i. For example, if a train bound for station N departs station i-1 at time t, the train arrives at station i exactly at time t+A_i.
• Assume that a train bound for station N arrives at a station at time s, and departs the station at time t. Then, the next train bound for station N arrives at the station at time s+K, and departs the station at time t+K. Additionally, the previous train bound for station N arrives at the station at time s-K, and departs the station at time t-K. This must also be true for trains bound for station 0.
• Trains running in opposite directions must not be running on the same single-tracked section (except the stations at both ends) at the same time.

Constraints

• 1 \leq N \leq 100000
• 1 \leq K \leq 10^9
• 1 \leq A_i \leq 10^9
• A_i is an integer.
• B_i is either 1 or 2.

Input

The input is given from Standard Input in the following format:

N K A_1 B_1 A_2 B_2 : A_N B_N

Output

Print an integer representing the minimum sum of the amount of time required for a train to depart station 0 and reach station N, and the amount of time required for a train to depart station N and reach station 0. If it is impossible to create a timetable satisfying the conditions, print -1 instead.

Examples

Input

3 10 4 1 3 1 4 1

Output

26

Input

1 10 10 1

Output

-1

Input

6 4 1 1 1 1 1 1 1 1 1 1 1 1

Output

12

Input

20 987654321 129662684 2 162021979 1 458437539 1 319670097 2 202863355 1 112218745 1 348732033 1 323036578 1 382398703 1 55854389 1 283445191 1 151300613 1 693338042 2 191178308 2 386707193 1 204580036 1 335134457 1 122253639 1 824646518 2 902554792 2

Output

14829091348

inputFormat

Input

The input is given from Standard Input in the following format:

N K A_1 B_1 A_2 B_2 : A_N B_N

outputFormat

Output

Print an integer representing the minimum sum of the amount of time required for a train to depart station 0 and reach station N, and the amount of time required for a train to depart station N and reach station 0. If it is impossible to create a timetable satisfying the conditions, print -1 instead.

Examples

Input

3 10 4 1 3 1 4 1

Output

26

Input

1 10 10 1

Output

-1

Input

6 4 1 1 1 1 1 1 1 1 1 1 1 1

Output

12

Input

20 987654321 129662684 2 162021979 1 458437539 1 319670097 2 202863355 1 112218745 1 348732033 1 323036578 1 382398703 1 55854389 1 283445191 1 151300613 1 693338042 2 191178308 2 386707193 1 204580036 1 335134457 1 122253639 1 824646518 2 902554792 2

Output

14829091348

样例

3 10
4 1
3 1
4 1

26