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c++ solution
use an array as index of a multi-base on different digit number

vector<int> dimension = getDim();
	//subtract 1 from every dimension to use as index
	for (int idx = 0; idx < dimension.size(); idx++) {
		dimension[idx]--;
	}
	
	//use as the array of index pass to getElement
	vector<int> idxV = dimension;
	long retSum = 0;
	while(true) {
		int idx = 0;
		//update index array
		while(true) {
			//all iteration are done. return sum
			if (idx >= dimension.size())
				return retSum;

			if (idxV[idx] == 0) {
				idxV[idx] = dimension[idx];
				idx++;
			} else {
				idxV[idx]--;
				break;
			}
		}

		retSum += getElement(idxV);
	}

recusive solution in c++

int sumMatrix(Matrix m) {
  vector<int> dim = m.getDim();
  vector<int> index;
  return partialSum(m, dim, index);
}

int partialSum(Matrix &m, vector<int> &dim, vector<int> &index) {
  int currDim = index.size();
  if (currDim == dim.size())
    return m.getElem(index);
    int sum = 0;
  for(int i = 0; i < dim[currDim]; i++) {
    index.push_back(i);
    sum += partialSum(m, dim, index);
    index.pop_back();
  }
  return sum;
}

public static void solve(int i, int dim[]){
if(i<0){
cnt++;
for(int x: dim){
System.out.print(x+" ");
}
System.out.println();
return;
}
solve(i-1, dim);
if(dim[i]>0) {
dim[i]--;
solve(i, dim);
dim[i]++;
}
}