Time Limit: 24000/12000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)

Round-table conferences were held around the round table, ensuring equal participations for leaders and attendants. It’s a custom holding the belief that “All men are created equal”, derived from the British story of King Arthur and his round table knights.

One day, Zero, as a sponsor holding a round-table conference, faces a tough problem. He knows that there are n groups of people (groups are labeled from 0 to n - 1) and m seats around the table (seats are labeled from 0 to m - 1) in the conference. There are a_{i} people in the i-th group. They should be assigned seats within range (l_{i}, (l_{i} + 1)%m, (l_{i}+ 2)%m, . . . , r_{i}).In a valid arrangment, everyone has a single seat, and no seat can be shared by more than one person. Zero wants to know whether such an arrangement exists.

One day, Zero, as a sponsor holding a round-table conference, faces a tough problem. He knows that there are n groups of people (groups are labeled from 0 to n - 1) and m seats around the table (seats are labeled from 0 to m - 1) in the conference. There are a

There are several test cases. Please process till EOF.

For each test case, The first line consists two numbers n(1 ≤ n ≤ 10^{5}) and m(1 ≤ m ≤ 10^{9}). Then follow n lines, each containing three numbers l_{i}, r_{i}(0 ≤ l_{i}, r_{i}< m) and a_{i}(1 ≤ a_{i} ≤ 10^{9}).

For each test case, The first line consists two numbers n(1 ≤ n ≤ 10

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