#U1718FS1. Rest Stops
Rest Stops
Farmer John and his personal trainer Bessie are hiking up Mount Vancowver. For their purposes (and yours), the mountain can be represented as a long straight trail of length LL meters (1≤L≤1061≤L≤106). Farmer John will hike the trail at a constant travel rate of rFrF seconds per meter (1≤rF≤1061≤rF≤106). Since he is working on his stamina, he will not take any rest stops along the way.Bessie, however, is allowed to take rest stops, where she might find some tasty grass. Of course, she cannot stop just anywhere! There are NN rest stops along the trail (1≤N≤1051≤N≤105); the ii-th stop is xixi meters from the start of the trail (0<xi**<L0<xi<L) and has a tastiness value cici (1≤ci≤1061≤ci≤106). If Bessie rests at stop ii for tt seconds, she receives ci⋅**tci⋅t tastiness units.
When not at a rest stop, Bessie will be hiking at a fixed travel rate of rBrB seconds per meter (1≤rB≤1061≤rB≤106). Since Bessie is young and fit, rBrB is strictly less than rFrF.
Bessie would like to maximize her consumption of tasty grass. But she is worried about Farmer John; she thinks that if at any point along the hike she is behind Farmer John on the trail, he might lose all motivation to continue!
Help Bessie find the maximum total tastiness units she can obtain while making sure that Farmer John completes the hike.
INPUT FORMAT (file reststops.in):
The first line of input contains four integers: LL, NN, rFrF, and rBrB. The next NN lines describe the rest stops. For each ii between 11 and NN, the i+1i+1-st line contains two integers xixi and cici, describing the position of the ii-th rest stop and the tastiness of the grass there.It is guaranteed that rF**>rBrF>rB, and 0<x1<⋯<xN**<L0<x1<⋯<xN<L. Note that rFrF and rBrB are given in seconds per meter!
OUTPUT FORMAT (file reststops.out):
A single integer: the maximum total tastiness units Bessie can obtain.
SAMPLE INPUT:
10 2 4 3
7 2
8 1
SAMPLE OUTPUT:
15
In this example, it is optimal for Bessie to stop for 77 seconds at the x=7x=7 rest stop (acquiring 1414 tastiness units) and then stop for an additional 11 second at the x=8x=8 rest stop (acquiring 11 more tastiness unit, for a total of 1515 tastiness units).