you give array distinct positive integer location locationsi represent position city you give integer start finish fuel represent start city end city initial fuel respectivelyAt step city pick city j j 0 j locationslength city j move city city j reduce fuel locationsi locationsj please notice x denote absolute value xNotice fuel negative point time allow visit city include start finishReturn count possible route start finish since answer large return modulo 109 7 Example 1input location 23684 start 1 finish 3 fuel 5output 4explanation the follow possible route use 5 unit fuel1 31 2 31 4 31 4 2 3example 2input location 431 start 1 finish 0 fuel 6output 5explanation the follow possible routes1 0 fuel 11 2 0 fuel 51 2 1 0 fuel 51 0 1 0 fuel 31 0 1 0 1 0 fuel 5Example 3input location 521 start 0 finish 2 fuel 3output 0explanation it impossible 0 2 3 unit fuel short route need 4 unit fuel constraints2 locationslength 1001 locationsi 109All integers location distinct0 start finish locationslength1 fuel 200