Problem: Tomorrow Peter has a Biology exam. He does not like this subject much, but d days ago he learnt that he would have to take this exam. Peter's strict parents made him prepare for the exam immediately, for this purpose he has to study not less than minTimei and not more than maxTimei hours per each i-th day. Moreover, they warned Peter that a day before the exam they would check how he has followed their instructions.

So, today is the day when Peter's parents ask him to show the timetable of his preparatory studies. But the boy has counted only the sum of hours sumTime spent him on preparation, and now he wants to know if he can show his parents a timetable sсhedule with d numbers, where each number sсhedulei stands for the time in hours spent by Peter each i-th day on biology studies, and satisfying the limitations imposed by his parents, and at the same time the sum total of all schedulei should equal to sumTime.

Input

The first input line contains two integer numbers d, sumTime (1 ≤ d ≤ 30, 0 ≤ sumTime ≤ 240) — the amount of days, during which Peter studied, and the total amount of hours, spent on preparation. Each of the following d lines contains two integer numbers minTimei, maxTimei (0 ≤ minTimei ≤ maxTimei ≤ 8), separated by a space — minimum and maximum amount of hours that Peter could spent in the i-th day.

Output

In the first line print YES, and in the second line print d numbers (separated by a space), each of the numbers — amount of hours, spent by Peter on preparation in the corresponding day, if he followed his parents' instructions; or print NO in the unique line. If there are many solutions, print any of them.

Examples

Input

1 48
5 7


Output

NO


Input

2 5
0 1
3 5


Output

YES
1 4 

Solution (in PYTHON3):

Solution:
import copy
def main():
       #get the number of days for studing and the total spent hours for studing in this days
       days, spentHours = map(int,input().split())
       minHours = [0]*days
       maxHours = [0]*days
       #for each day save the number of min hours to spend on studing
       #and the number of maximal hours
       for i in range(days):
              minHours[i] , maxHours[i] = map(int,input().split())
       #if sum(minHours) <= spentHours <= sum(maxHours) then student accomplished parents requirements
       #we check the opposite condition, because if student didn't accomplished the requirements we just print NO and stop
       if not (sum(minHours) <= spentHours and spentHours <= sum(maxHours)):
              print('NO')
              return
       else: #if he did spend necessary amount of hours, than we have to make a list with possible hours that he spent daily
              #we know that he spent at least min hours daily
              #so we put in the spentDailyHours the minHours
              spentDailyHours = copy.deepcopy(minHours)
              #and substract them form spentHours, the remaining hours we have to spread between remaining days
              spentHours -= sum(minHours)
              print('YES')
              #here we spread the remaining hours in available days 
              for i in range(days):
                     #first we check if there are remaining hours
                     if spentHours > 0:
                            #and if the remaining hours + minHours are more than maxHours 
                            if spentHours > maxHours[i] - minHours[i]:
                                   #this means that in this day he spent maxHours on studing
                                   spentDailyHours[i] = maxHours[i]
                                   #and we substract them form spentHours
                                   spentHours -= maxHours[i] - minHours[i]
                            else:
                                   #if the remaining hours + minHours are less or equal to maxHours
                                   # this means that we can add them to the current day and stop, because there will be no more spentHours 
                                   spentDailyHours[i] += spentHours
                                   break
                     else:#if there are no remaining hours, stop
                            break
              #print the results in the desired form
              for time in spentDailyHours:
                     print(time, end=" ")
main()