Masters Tournament- - Saving Snuuk

Kenkoooo is planning a trip in Republic of Snuke. In this country, there are n cities and m trains running. The cities are numbered 1 through n, and the i-th train connects City u_i and v_i bidirectionally. Any city can be reached from any city by changing trains.

Two currencies are used in the country: yen and snuuk. Any train fare can be paid by both yen and snuuk. The fare of the i-th train is a_i yen if paid in yen, and b_i snuuk if paid in snuuk.

In a city with a money exchange office, you can change 1 yen into 1 snuuk. However, when you do a money exchange, you have to change all your yen into snuuk. That is, if Kenkoooo does a money exchange when he has X yen, he will then have X snuuk. Currently, there is a money exchange office in every city, but the office in City i will shut down in i years and can never be used in and after that year.

Kenkoooo is planning to depart City s with 10^{15} yen in his pocket and head for City t, and change his yen into snuuk in some city while traveling. It is acceptable to do the exchange in City s or City t.

Kenkoooo would like to have as much snuuk as possible when he reaches City t by making the optimal choices for the route to travel and the city to do the exchange. For each i=0,...,n-1, find the maximum amount of snuuk that Kenkoooo has when he reaches City t if he goes on a trip from City s to City t after i years. You can assume that the trip finishes within the year.

Constraints

• 2 \leq n \leq 10^5
• 1 \leq m \leq 10^5
• 1 \leq s,t \leq n
• s \neq t
• 1 \leq u_i < v_i \leq n
• 1 \leq a_i,b_i \leq 10^9
• If i\neq j, then u_i \neq u_j or v_i \neq v_j.
• Any city can be reached from any city by changing trains.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

n m s t u_1 v_1 a_1 b_1 : u_m v_m a_m b_m

Output

Print n lines. In the i-th line, print the maximum amount of snuuk that Kenkoooo has when he reaches City t if he goes on a trip from City s to City t after i-1 years.

Examples

Input

4 3 2 3 1 4 1 100 1 2 1 10 1 3 20 1

Output

999999999999998 999999999999989 999999999999979 999999999999897

Input

8 12 3 8 2 8 685087149 857180777 6 7 298270585 209942236 2 4 346080035 234079976 2 5 131857300 22507157 4 8 30723332 173476334 2 6 480845267 448565596 1 4 181424400 548830121 4 5 57429995 195056405 7 8 160277628 479932440 1 6 475692952 203530153 3 5 336869679 160714712 2 7 389775999 199123879

Output

999999574976994 999999574976994 999999574976994 999999574976994 999999574976994 999999574976994 999999574976994 999999574976994

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

n m s t u_1 v_1 a_1 b_1 : u_m v_m a_m b_m

outputFormat

Output

Print n lines. In the i-th line, print the maximum amount of snuuk that Kenkoooo has when he reaches City t if he goes on a trip from City s to City t after i-1 years.

Examples

Input

4 3 2 3 1 4 1 100 1 2 1 10 1 3 20 1

Output

999999999999998 999999999999989 999999999999979 999999999999897

Input

8 12 3 8 2 8 685087149 857180777 6 7 298270585 209942236 2 4 346080035 234079976 2 5 131857300 22507157 4 8 30723332 173476334 2 6 480845267 448565596 1 4 181424400 548830121 4 5 57429995 195056405 7 8 160277628 479932440 1 6 475692952 203530153 3 5 336869679 160714712 2 7 389775999 199123879

Output

999999574976994 999999574976994 999999574976994 999999574976994 999999574976994 999999574976994 999999574976994 999999574976994

样例

8 12 3 8
2 8 685087149 857180777
6 7 298270585 209942236
2 4 346080035 234079976
2 5 131857300 22507157
4 8 30723332 173476334
2 6 480845267 448565596
1 4 181424400 548830121
4 5 57429995 195056405
7 8 160277628 479932440
1 6 475692952 203530153
3 5 336869679 160714712
2 7 389775999 199123879

999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994

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