The Fry King is a small criminal mastermind from the western european nation of Belgium, more specifically Flanders. He has acquired every single fastfood restaurant in a large part of Belgium and set them out on a 101X49 grid (102 intersections horizontally, 50 vertically, including the borders), 5100 restaurants in total located on the intersections. The next step in his diabolical plan is to orchestrate the closing hours of these restaurants so that on any one day of the year (bar 2 explained later), only 1 corner of each square will have an open restaurant.
Example with a 6X2 grid:
1---2---3---4---1---2 | | | | | | 3---4---1---2---3---4
A year has 365 days. On the first Monday of the year, only the restaurants with number 1 will be open. On the next day, Tuesday, only those with the number 2. On the next day, Wednesday, only those with number 3. On the next day, Thursday, only those with number 4. after that, it starts again at 1. The days before the first Monday count back. For example, if the first Monday falls on January 3rd, the Sunday before the 4s will be open. This might mean that when the year changes, a store might be open twice or might be skipped in the rotation.
There are 2 exceptions: the 21st of July is the national holiday. All restaurants are open. Another is the 29th of February. Because this is the Fry King's birthday, all restaurants are also open. These exceptions replace a normal day, so if the 20th is for the restaurant with number 1, the 22nd is for the joints with number 3.
You are a vigilante coder who has setup a toll-free texting number. It accepts 3 values, delimited by an *: A number between 1 and 101 denoting the column value you're in, a number between 1 and 49 to denote the row number you're in (these 2 determine which joints are eligible) and a date in the format of DD/MM/YYYY (day/month/year). The number returns 2 letters indicating which corner of your square contains today's open restaurant (NW-NE-SE-SW). If there are multiple options, it returns the first eligible one from the previous series.
Calculation is code golf. Shortest code in bytes wins. There are no special bonuses to win or limitations involved, apart from 1: no external resources.