This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <stdio.h>
#include<vector>
#include <algorithm>
#include <map>
using namespace std;
typedef long long ll;
const int MX = 3005, MM = 1000000007;
ll pw(ll A, ll B){
ll R = 1;
while(B){
if( B&1 ) R = R * A % MM;
A = A * A % MM; B /= 2;
}
return R;
}
ll rv(ll A){ return pw(A, MM-2); }
struct frac{
ll A, B;
frac(ll A):A(A), B(1){}
frac(ll a, ll b){
A = (a%MM+MM) % MM;
B = (b%MM+MM) % MM;
}
frac(){A = 0, B = 1;}
frac operator+ (const frac &l)const{
return frac((A * l.B + B * l.A) % MM, B * l.B % MM);
}
frac operator*(const frac &l)const{
return frac(A*l.A % MM, B*l.B % MM);
}
frac operator/(const frac &l)const{
return frac(A*l.B % MM, B*l.A % MM);
}
frac operator- (const frac &l)const{
return frac((A*l.B - B*l.A%MM + MM) % MM, B*l.B % MM);
}
ll v(){ return A * rv(B) % MM; }
};
frac pw(frac A, ll B){
frac R = 1;
while(B){
if( B&1 ) R = R * A;
A = A * A; B /= 2;
}
return R;
}
frac F[MX], _5[MX];
int main()
{
F[0] = 1; _5[0] = frac(1, 1);
for(int i = 1; i <= 1000; i++) F[i] = F[i-1] * i, _5[i] = _5[i-1] * frac(1, 2);
int H, W;
scanf("%d%d", &H, &W);
frac A = 0, B = 0, C = 0;
for(int i = 1; i <= W; i++){
for(int j = 1; j <= W-i; j++){
int k = W-i-j;
A = A + F[W] / F[i] / F[j] / F[k] * (
pw(_5[i] + _5[j] + 1, H)
- pw(_5[i] + 1, H)
- pw(_5[j] + 1, H)
+ 1
);
}
}
for(int i = 1; i <= W; i++){
for(int j = 1; j <= W-i; j++){
int k = W-i-j;
B = B + F[W] / F[i] / F[j] / F[k] * (
pw(_5[i] + _5[j] + _5[i+j] + 1, H)
- pw(_5[i] + _5[j] + 1, H)
);
}
}
for(int i = 1; i <= H; i++){
for(int j = 1; j <= H-i; j++){
int k = H-i-j;
C = C + F[H] / F[i] / F[j] / F[k] * (
pw(_5[i] + _5[j] + _5[i+j] + 1, W)
- pw(_5[i] + _5[j] + 1, W)
);
}
}
frac ans = B + C + A;
if( ans.A == 0 && ans.B == 0 ) for(;;);
printf("%lld\n", ans.v());
}
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