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src/atcoders/abc/abc342/e/problem.md

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+In the country of AtCoder, there are 
+N stations: station 
+1, station 
+2, 
+…, station 
+N.
+
+You are given 
+M pieces of information about trains in the country. The 
+i-th piece of information 
+(1≤i≤M) is represented by a tuple of six positive integers 
+(l 
+i
+​
+ ,d 
+i
+​
+ ,k 
+i
+​
+ ,c 
+i
+​
+ ,A 
+i
+​
+ ,B 
+i
+​
+ ), which corresponds to the following information:
+
+For each 
+t=l 
+i
+​
+ ,l 
+i
+​
+ +d 
+i
+​
+ ,l 
+i
+​
+ +2d 
+i
+​
+ ,…,l 
+i
+​
+ +(k 
+i
+​
+ −1)d 
+i
+​
+ , there is a train as follows:
+The train departs from station 
+A 
+i
+​
+  at time 
+t and arrives at station 
+B 
+i
+​
+  at time 
+t+c 
+i
+​
+ .
+No trains exist other than those described by this information, and it is impossible to move from one station to another by any means other than by train.
+Also, assume that the time required for transfers is negligible.
+
+Let 
+f(S) be the latest time at which one can arrive at station 
+N from station 
+S.
+More precisely, 
+f(S) is defined as the maximum value of 
+t for which there is a sequence of tuples of four integers 
+((t 
+i
+​
+ ,c 
+i
+​
+ ,A 
+i
+​
+ ,B 
+i
+​
+ )) 
+i=1,2,…,k
+​
+  that satisfies all of the following conditions:
+
+t≤t 
+1
+​
+
+A 
+1
+​
+ =S,B 
+k
+​
+ =N
+B 
+i
+​
+ =A 
+i+1
+​
+  for all 
+1≤i<k,
+For all 
+1≤i≤k, there is a train that departs from station 
+A 
+i
+​
+  at time 
+t 
+i
+​
+  and arrives at station 
+B 
+i
+​
+  at time 
+t 
+i
+​
+ +c 
+i
+​
+ .
+t 
+i
+​
+ +c 
+i
+​
+ ≤t 
+i+1
+​
+  for all 
+1≤i<k.
+If no such 
+t exists, set 
+f(S)=−∞.
+
+Find 
+f(1),f(2),…,f(N−1).