output_description: If Nakahashi can take in at most c kilocalories on balance before he leaves
  the restaurant, print c.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N C
      x_1 v_1
      x_2 v_2
      :
      x_N v_N
attempt: # coding: utf-8
  n, c = map(int, input().split())
  lane_r = []
  lane_l = []
  for i in range(n):
      a, b = map(int, input().split())
      lane_r.append((a, b))
      lane_l.append((c - a, b))
  lane_l = lane_l[::-1]
  acm_lane_r = [0]
  acm_lane_l = [0]
  for i in range(n):
      acm_lane_r.append(acm_lane_r[-1] + lane_r[i][1])
      acm_lane_l.append(acm_lane_l[-1] + lane_l[i][1])
  for i in range(1, n + 1):
      acm_lane_r[i] -= lane_r[i - 1][0]
      acm_lane_l[i] -= lane_l[i - 1][0]
  mxl = 0
  mxr = 0
  pl = 0
  pr = 0
  for i in range(n + 1):
      if mxl < acm_lane_l[i]:
          mxl = acm_lane_l[i]
          pl = lane_l[i - 1][0]
      acm_lane_l[i] = (mxl, pl)
      if mxr < acm_lane_r[i]:
          mxr = acm_lane_r[i]
          pr = lane_r[i - 1][0]
      acm_lane_r[i] = (mxr, pr)
  mx = 0
  lane_r.insert(0, (0, 0))
  lane_l.insert(0, (0, 0))
  for i in range(n + 1):
      mx = max(
          acm_lane_r[n - i][0]
          + acm_lane_l[i][0]
          - min(acm_lane_r[n - i][1], acm_lane_l[i][1]),
          mx,
      )
  for i in range(n + 1):
      mx = max(
          acm_lane_l[n - i][0]
          + acm_lane_r[i][0]
          - min(acm_lane_l[n - i][1], acm_lane_r[i][1]),
          mx,
      )
  print(mx)
  
problem_description: Statement
  
  "Teishi-zushi", a Japanese restaurant, is a plain restaurant with only one
  round counter. The outer circumference of the counter is C meters. Customers
  cannot go inside the counter.
  
  Nakahashi entered Teishi-zushi, and he was guided to the counter. Now, there
  are N pieces of sushi (vinegared rice with seafood and so on) on the counter.
  The distance measured clockwise from the point where Nakahashi is standing to
  the point where the i-th sushi is placed, is x_i meters. Also, the i-th sushi
  has a nutritive value of v_i kilocalories.
  
  Nakahashi can freely walk around the circumference of the counter. When he
  reach a point where a sushi is placed, he can eat that sushi and take in its
  nutrition (naturally, the sushi disappears). However, while walking, he
  consumes 1 kilocalories per meter.
  
  Whenever he is satisfied, he can leave the restaurant from any place (he does
  not have to return to the initial place). On balance, at most how much
  nutrition can he take in before he leaves? That is, what is the maximum
  possible value of the total nutrition taken in minus the total energy
  consumed? Assume that there are no other customers, and no new sushi will be
  added to the counter. Also, since Nakahashi has plenty of nutrition in his
  body, assume that no matter how much he walks and consumes energy, he never
  dies from hunger.
samples: [{"input": "3 20\n    2 80\n    9 120\n    16 1", "output": "191\n    \n\nThere are three sushi on the counter with a circumference of 20 meters. If he\nwalks two meters clockwise from the initial place, he can eat a sushi of 80\nkilocalories. If he walks seven more meters clockwise, he can eat a sushi of\n120 kilocalories. If he leaves now, the total nutrition taken in is 200\nkilocalories, and the total energy consumed is 9 kilocalories, thus he can\ntake in 191 kilocalories on balance, which is the largest possible value.\n\n* * *"}, {"input": "3 20\n    2 80\n    9 1\n    16 120", "output": "192\n    \n\nThe second and third sushi have been swapped. Again, if he walks two meters\nclockwise from the initial place, he can eat a sushi of 80 kilocalories. If he\nwalks six more meters counterclockwise this time, he can eat a sushi of 120\nkilocalories. If he leaves now, the total nutrition taken in is 200\nkilocalories, and the total energy consumed is 8 kilocalories, thus he can\ntake in 192 kilocalories on balance, which is the largest possible value.\n\n* * *"}, {"input": "1 100000000000000\n    50000000000000 1", "output": "0\n    \n\nEven though the only sushi is so far that it does not fit into a 32-bit\ninteger, its nutritive value is low, thus he should immediately leave without\ndoing anything.\n\n* * *"}, {"input": "15 10000000000\n    400000000 1000000000\n    800000000 1000000000\n    1900000000 1000000000\n    2400000000 1000000000\n    2900000000 1000000000\n    3300000000 1000000000\n    3700000000 1000000000\n    3800000000 1000000000\n    4000000000 1000000000\n    4100000000 1000000000\n    5200000000 1000000000\n    6600000000 1000000000\n    8000000000 1000000000\n    9300000000 1000000000\n    9700000000 1000000000", "output": "6500000000\n    \n\nAll these sample inputs above are included in the test set for the partial\nscore."}]