Blaise was about to enter Amber, but Julian's army began to bombard his army from the city walls. Blaze is not stupid and understands that while Julian's army is shelling his soldiers, they will not be able to collect siege weapons, so the defenders of the walls must be destroyed.
Blaise and Julian form their archery squads in a line and give each squad a number from 1 to n. Each unit has its own strength, which is expressed by some natural number.
In front of Julian's squad number i is Blaze's squad number i. Followed by m orders:
Julian orders squads l1 to r1 to fire a salvo at Blaze's squads facing them .
While Julian's arrows are reloading, Blaze orders units numbered from l2 to r2 fire a volley at Julian's arrows opposite.
After that, everything repeats: Julian fires a volley, Blaze fires a volley, etc.
The strength of a volley and defense are calculated as the sum of the forces of soldiers on the segment [l; r]. If the strength of a volley is higher than defense, then all defending units are destroyed and can no longer shoot (their strength is no longer taken into account when calculating defense and volley strength).
You have been given orders of commanders. Your task is to find out whose army won. The winning army is the one that, after the last order, can destroy the enemy army, i.e. volley strength on segment [1; n] of the winning army is greater than the defense of the losing army on the segment [1; n].
If Blaze wins, print "Bleys" (without quotes).
Otherwise print "
Julian" (without quotes). Also print the difference between the strength of the volley of the winning army and the defense of the losing one.
Input
The first line contains the numbers n and m (1 <= n, m <= 100000) - the number of units Blaise and Julian have and the number of units given orders.
The second line contains n numbers a1, a2, ..., an (1 <= ai < = 1000) - the strength of Julian's units.
The third line contains
n numbers
b1,
b2,
..., b
n (1 <= bi <= 1000) - strength of Blaze's troops.
The following
m lines contain numbers
l and
r (1 <= l <= r <= n) - given orders.
Imprint
Print "
Bleys" if Blaze won. Otherwise print "
Julian". Also print a number - the difference between the strength of the volley and the defense.
Examples
| # |
Input |
Output |
| 1 |
10 3
2 2 4 9 1 8 6 1 8 8
1 1 8 9 3 6 5 1 8 6
5 9
16
9 10
|
Julian 30 |