/*
* Calculates the matrix that transforms a B-spline basis to a power basis
* Input: p (degree of basis)
* Output: M (power matrix)
*/
DenseMatrix getBSplineToPowerBasisMatrix1D(unsigned int p)
{
assert(p > 0); // m = n+p+1
// M is a lower triangular matrix of size (p+1)x(p+1)
DenseMatrix M; M.setZero(p+1,p+1);
for (unsigned int j = 0; j <= p; j++) // cols
{
for (unsigned int i = j; i <= p; i++) // rows
{
M(i,j) = pow(-1,i-j)*binomialCoeff(p,j)*binomialCoeff(p-j,i-j);
}
}
return M;
}
int main()
{
int n,k,t;
scanf("%d",&t);
while(t--)
{
scanf("%d%d",&n,&k);
printf("%lld\n",binomialCoeff(n+k-1,n-1));
}
return 0;
}
/*
* Calculates the reparameterization matrix that changes the domain of a basis
* Input: p (degree of basis), a (left bound/first knot), b (right bound/last knot)
* Output: Rinv (reparameterization matrix that changes the domain from [0,1] to [a,b])
*/
DenseMatrix getReparameterizationMatrix1D(int p, double a, double b)
{
assert(p > 0 && a < b);
// R is a upper triangular matrix of size (p+1)x(p+1)
DenseMatrix R; R.setZero(p+1,p+1);
for (int i = 0; i <= p; i++) // rows
{
for (int j = i; j <= p; j++) // cols
{
R(i,j) = binomialCoeff(j,i)*pow(b-a,i)*pow(a,j-i);
}
}
return R;
}
// This function returns an array of nCm integers. In each integer, exactly m bits are 1.
int *subsets(int n, int m)
{
int maxsubsetindex; // maximum subset index
int count;
int shiftedx;
int c,C;
int *subsetlist;
if(m>n)
{
printf("\n\nError: m must be less than or equal to n.\n\n");
return(NULL);
}
if( n >= 8*sizeof(int))
{
printf("\n\nError: n must be less than %d.\n\n",8*sizeof(int));
return(NULL);
}
maxsubsetindex = (int)pow(2.0,1.0*n)-1;
C = binomialCoeff(n,m);
subsetlist = (int *)calloc(C,sizeof(int));
c = 0;
for(int x=0; x<=maxsubsetindex; x++)
{
count=0;
for(int i=0; i<n; i++)
{
shiftedx = x >> i;
count += (shiftedx & 1);
}
if(count==m) subsetlist[c++]=x;
}
return(subsetlist);
}
int main(){
int n,k;
scanf("%d%d",&n,&k);
printf("%d",binomialCoeff(n,k));
return 0;
}
