int64_t step(int64_t tape, int64_t width, int64_t height){
	if(tape == 0){
        return 0;
    }

    if(tape >= width * height -1){
        return full(width, height);
    } else {
    	if(width == 2){
        	int64_t tapeHeightDiff = tape - height;
        	if(tapeHeightDiff <= 0){
            	return ((tape * tape * tape) -1);
        	}
        	return ((tape * tape * tape)-1 - (tapeHeightDiff*(tapeHeightDiff+1)));
    	}
	    int64_t sum = 0;
	    for(int64_t i = 0; i < min(height, tape); i++){
	        sum += (step(tape-i, width-1, height)) % mod;
	    }
	    if(min(height,tape) == tape){
	        sum++ %mod;
	    } else {
	        sum += (step(tape-height,width-1,height)) % mod;
	    }
	    return sum % mod;
	}
}