Codeforces Round #313 (Div. 1) C. Gerald and Giant Chess

 1 #include<cstdio>
 2 #include<algorithm>
 3 #include<map>
 4 #include<cstring>
 5 #include<vector>
 6 #include<cmath>
 7 #include<iostream>
 8 #include<string>
 9 #define N 600010
10 #define M 1010
11 #define P 1000000007
12 using namespace std;
13 struct Q{
14     int x,y,z;
15 }a[N];
16 int h,w,n,i,j;
17 long long g[N],sum[N];
18 int exgcd(int a,int b,long long &x,long long &y)
19 {
20     long long t;
21     if (b==0)
22     {
23         x=1;y=0;return a;
24     }   
25     exgcd(b,a%b,x,y);
26     t=x;
27     x=y;
28     y=t-a/b*y;
29 }
30 long long cl(int x,int y)
31 {
32     long long a,b,z,zz;
33     z=x+y-2;
34     zz=g[x-1]*g[z-x+1]%P;
35     z=g[z];
36     exgcd(zz,P,a,b);
37     z=(z*a%P+P)%P;
38     return z;
39 }
40 bool cmp(Q a,Q b)
41 {
42     return a.z<b.z;
43 }
44 int main()
45 {
46     scanf("%d%d%d",&h,&w,&n); 
47     g[0]=1;
48     for (i=1;i<=200000;i++)
49     g[i]=(g[i-1]*i)%P;
50     for (i=1;i<=n;i++)
51     {
52         scanf("%d%d",&a[i].x,&a[i].y);
53         a[i].z=a[i].x+a[i].y;
54     }
55     a[n+1].x=h;a[n+1].y=w;a[n+1].z=h+w;
56     sort(a+1,a+1+n+1,cmp);
57     for (i=1;i<=n+1;i++)
58     {
59         sum[i]=cl(a[i].x,a[i].y);
60         for (j=1;j<i;j++)
61         if ((a[j].x<=a[i].x)&&(a[j].y<=a[i].y))
62         sum[i]=(sum[i]-sum[j]*cl(a[i].x-a[j].x+1,a[i].y-a[j].y+1))%P;
63     }
64     sum[n+1]=(sum[n+1]%P+P)%P;
65     printf("%I64d\n",sum[n+1]);
66 }