fast robot

#include <algorithm>
#include <iostream>
#include <sstream>
#include <string>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <cstdio>
#include <cstdlib>
#include <cctype>
#include <cmath>
#include <cstring>
using namespace std;
typedef unsigned long long LL;
#define FOR(k,a,b) for(int k(a); k < (b); ++k)
#define FORD(k,a,b) for(int k(a-1); k >= (b); --k)
#define REP(k,a) for(int k=0; k < (a); ++k)
#define ABS(a) ((a)>0?(a):-(a))
const int mod=1e9+7;
const int mSize=5002;

char *ipos, *opos, InpFile[200000], OutFile[200000];
inline int readInt()
{
    while(*ipos <= 32) ++ipos;
    int x=0;
    char c;
    while( 1 )
    {
        c=*ipos++;
        if (c<=32) return x;
        x*=10;
        x+=c-'0';
    }
}

inline void writeInt(int a)
{
    opos+=sprintf(opos,"%d\n",a);
}

inline void InitIO() {
    ipos = InpFile;
    opos = OutFile;
    fread_unlocked(InpFile,200000,1,stdin);
}
inline void FlushIO() {
    fwrite_unlocked(OutFile,opos-OutFile,1,stdout);
}

int inverse(int a)
{
    int n=mod-2;
    LL tmp=a,res=1;
    while(n)
    {
        if(n&1)
            res*=tmp;
        res%=mod;
        n>>=1;
        tmp*=tmp;
        tmp%=mod;
    }
    return res;
}

int main()
{
    int inv[mSize],fact[mSize];
    fact[0]=1;
    inv[0]=1;
    FOR(i,1,mSize)
    {
        fact[i]=(fact[i-1]*(LL)i)%mod;
        inv[i]=inverse(fact[i]);
    }
    InitIO();
    int N,K,K1,K2;
    LL res=0;
    while(true)
    {
        /*scanf("%d %d",&N,&K);*/
        N=readInt();
        K=readInt();
        if(N==0 && K==0)
            break;
        if(N==1 || K>2*N-3)
        {
            //because k positive
            writeInt(0);
            continue;
        }
        --K;
        K1=K/2;
        K2=(K+1)/2;
        res=2LL*fact[N-2]*inv[K1];
        res%=mod;
        res*=inv[N-2-K1];
        res%=mod;
        res*=fact[N-2];
        res%=mod;
        res*=inv[K2];
        res%=mod;
        res*=inv[N-2-K2];
        res%=mod;
        writeInt(res);
    }
    FlushIO();
    return 0;
}