{"raw_statement":[{"iden":"problem statement","content":"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.\nTwo 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.\nIn 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.\nKenkoooo 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 $t$.\nKenkoooo 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."},{"iden":"constraints","content":"*   $2 \\leq n \\leq 10^5$\n*   $1 \\leq m \\leq 10^5$\n*   $1 \\leq s,t \\leq n$\n*   $s \\neq t$\n*   $1 \\leq u_i < v_i \\leq n$\n*   $1 \\leq a_i,b_i \\leq 10^9$\n*   If $i\\neq j$, then $u_i \\neq u_j $ or $v_i \\neq v_j$.\n*   Any city can be reached from any city by changing trains.\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$n$ $m$ $s$ $t$\n$u_1$ $v_1$ $a_1$ $b_1$\n$:$\n$u_m$ $v_m$ $a_m$ $b_m$"},{"iden":"sample input 1","content":"4 3 2 3\n1 4 1 100\n1 2 1 10\n1 3 20 1"},{"iden":"sample output 1","content":"999999999999998\n999999999999989\n999999999999979\n999999999999897\n\nAfter $0$ years, it is optimal to do the exchange in City $1$.  \nAfter $1$ years, it is optimal to do the exchange in City $2$.  \nNote that City $1$ can still be visited even after the exchange office is closed. Also note that, if it was allowed to keep $1$ yen when do the exchange in City $2$ and change the remaining yen into snuuk, we could reach City $3$ with $999999999999998$ snuuk, but this is NOT allowed.  \nAfter $2$ years, it is optimal to do the exchange in City $3$.  \nAfter $3$ years, it is optimal to do the exchange in City $4$. Note that the same train can be used multiple times."},{"iden":"sample input 2","content":"8 12 3 8\n2 8 685087149 857180777\n6 7 298270585 209942236\n2 4 346080035 234079976\n2 5 131857300 22507157\n4 8 30723332 173476334\n2 6 480845267 448565596\n1 4 181424400 548830121\n4 5 57429995 195056405\n7 8 160277628 479932440\n1 6 475692952 203530153\n3 5 336869679 160714712\n2 7 389775999 199123879"},{"iden":"sample output 2","content":"999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}