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| 10170 | |
| The Hotel with Infinite Rooms | |
| The city of HaluaRuti has a strange hotel with infinite rooms. The groups that come to this hotel | |
| follow the following rules: | |
| a) At the same time only members of one group can rent the hotel. | |
| b) Each group comes in the morning of the check-in day and leaves the hotel in the evening of the | |
| check-out day. | |
| c) Another group comes in the very next morning after the previous group has left the hotel. | |
| d) A very important property of the incoming group is that it has one more member than its previous | |
| group unless it is the starting group. You will be given the no of members of the starting group. | |
| e) A group with n members stays for n days in the hotel. For example, if a group of four members | |
| comes on 1st August in the morning, it will leave the hotel on 4th August in the evening and the | |
| next group of five members will come on 5th August in the morning and stay for five days and so | |
| on. | |
| Given the initial group size you will have to find the group size staying in the hotel on a specified | |
| day. | |
| Input | |
| The input contains round numbers S (1 ≤S ≤10000) and D (1 ≤D < 1015) in every line. S denotes | |
| the initial size of the group and D denotes that you will have to find the group size staying in the hotel | |
| on D-th day (starting from 1). All the input and output integers will be less than 1015. A group size S | |
| means that on the first day a group of S members come to the hotel and stays for S days then comes | |
| a group of S + 1 members according to the previously described rules and so on. | |
| Output | |
| For each line of input, print on a single line the size of the group staying in the hotel on the D-th day. | |
| Sample Input | |
| 1 6 | |
| 3 10 | |
| 3 14 | |
| Sample Output | |
| 3 | |
| 5 | |
| 6 |