Problem: For a given weighted graph G(V, E) and a source r, find the source shortest path to each vertex from the source (SSSP: Single Source Shortest Path).

Constraints

* 1 ≤ |V| ≤ 100000
* 0 ≤ di ≤ 10000
* 0 ≤ |E| ≤ 500000
* There are no parallel edges
* There are no self-loops

Input

An edge-weighted graph G (V, E) and the source r.


|V| |E| r
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1


|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively. r is the source of the graph.

si and ti represent source and target vertices of i-th edge (directed) and di represents the cost of the i-th edge.

Output

Print the costs of SSSP in the following format.


c0
c1
:
c|V|-1


The output consists of |V| lines. Print the cost of the shortest path from the source r to each vertex 0, 1, ... |V|-1 in order. If there is no path from the source to a vertex, print INF.

Examples

Input

4 5 0
0 1 1
0 2 4
1 2 2
2 3 1
1 3 5


Output

0
1
3
4


Input

4 6 1
0 1 1
0 2 4
2 0 1
1 2 2
3 1 1
3 2 5


Output

3
0
2
INF

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

// AOJ GRL_1_A Dijkstra O(E log V)
public class Main {

	private static Scanner sc;
	private static Printer pr;

	private static void solve() {
		int v = sc.nextInt();
		int e = sc.nextInt();
		int r = sc.nextInt();

		Dijkstra di = new Dijkstra(v);
		for (int i = 0; i < e; i++) {
			int s = sc.nextInt();
			int t = sc.nextInt();
			int d = sc.nextInt();
			di.addEdge(s, t, d);
		}

		for (int i = 0; i < v; i++) {
			long tmp = di.getShortestPathWeight(r, i);
			if (tmp != di.INF) {
				pr.println(tmp);
			} else {
				pr.println("INF");
			}
		}
	}

	/**
	 * Dijkstra法による重み付き有向グラフ上の単一始点最短路問題を解く
	 * 重みは非負でなければならない
	 * O(E logV)
	 */
	static class Dijkstra {
		long[] d;
		List<List<Edge>> edges;
		private PriorityQueue<Vertex> pq;
		private int n;
		private int s;
		int[] p;

		final long INF = Long.MAX_VALUE;

		/**
		 * n個の頂点を持つグラフに関するインスタンスを返す
		 * 
		 * @param n グラフの頂点数
		 */
		Dijkstra(int n) {
			this.n = n;

			edges = new ArrayList<>(n);
			for (int ii = 0; ii < n; ii++) {
				edges.add(new ArrayList<Edge>());
			}

			s = - 1;
		}

		/**
		 * グラフに有向辺(頂点 i から頂点 j へ)を追加する
		 * 無向グラフの場合は、逆向きも追加すること
		 * 
		 * @param i 有向辺の始点(from){@literal (0<=i<n)}
		 * @param j 有向辺の終点(to){@literal (0<=i<n)}
		 * @param c 有向辺の重み({@literal c>=0}でなければならない)
		 */
		public void addEdge(int i, int j, int c) {
			edges.get(i).add(new Edge(i, j, c));
		}

		/**
		 * 始点 i から終点 j までの最短路重みを返す
		 * 始点が同じ場合は前回の最短路結果を使い回す
		 * i を以前の呼び出しから変更した場合、最短路を計算しなおす(有向辺の情報はそのままで)
		 * 
		 * @param i 最短路を求める始点{@literal (0<=i<n)}
		 * @param j 最短路を求める終点{@literal (0<=j<n)}
		 * @return 最短路重み。始点から終点に到達できない場合、INF
		 */
		public long getShortestPathWeight(int i, int j) {
			if (s != i) {
				s = i;
				
				d = new long[n];
				Arrays.fill(d, INF);
				d[s] = 0;
				p = new int[n];
				Arrays.fill(p, -1);
				pq = new PriorityQueue<Vertex>();
				pq.add(new Vertex(s, d[s]));

				while (!pq.isEmpty()) {
					Vertex u = pq.poll();
					if (d[u.me] < u.d) {
						continue;  // skip old vertex
					}

					List<Edge> uu = edges.get(u.me);
					for (Edge v : uu) {
						if (d[u.me] == INF) {
						} else if (d[v.v] > d[u.me] + v.w) {
							d[v.v] = d[u.me] + v.w;
							pq.add(new Vertex(v.v, d[v.v]));
							p[v.v] = u.me;
						} else if (d[v.v] == d[u.me] + v.w) {
						}
					}
				}
			}

			return d[j];
		}

		/**
		 * 始点 i から終点 j までの最短路のうち1つを返す
		 * 始点が同じ場合は前回の最短路結果を使い回す
		 * i を以前の呼び出しから変更した場合、最短路を計算しなおす(有向辺の情報はそのままで)
		 * 
		 * @param i 最短路を求める始点{@literal (0<=i<n)}
		 * @param j 最短路を求める終点{@literal (0<=j<n)}
		 * @return 最短路を示す頂点の集合。始点から終点に到達できない場合、null
		 */
		public List<Integer> getShortestPath(int i, int j) {
			if (s != i) {
				getShortestPathWeight(i, j);
			}

			if (d[j] == INF) {
				return null;
			}
			
			List<Integer> ret = new ArrayList<>();
			ret.add(j);
			while (p[j] >= 0) {
				j = p[j];
				ret.add(j);
			}
			Collections.reverse(ret);
			
			return ret;
		}

		private static class Edge {
//			int u; // from
			int v; // to
			int w; // cost

			Edge(int u, int v, int w) {
//				this.u = u;
				this.v = v;
				this.w = w;
			}
		}

		private static class Vertex implements Comparable<Vertex> {
			int me; // me
			long d; // cost

			Vertex(int u, long w) {
				this.me = u;
				this.d = w;
			}

			@Override
			public int compareTo(Vertex o) {
				return Long.compare(d, o.d);
			}
		}
	}

	// ---------------------------------------------------
	public static void main(String[] args) {
		sc = new Scanner(INPUT == null ? System.in : new ByteArrayInputStream(INPUT.getBytes()));
		pr = new Printer(System.out);

		solve();

//		pr.close();
		pr.flush();
//		sc.close();
	}

	static String INPUT = null;

	@SuppressWarnings("unused")
	private static class Scanner {
		BufferedReader br;

		Scanner (InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
		}

		private boolean isPrintable(int ch) {
			return ch >= '!' && ch <= '~';
		}

		private boolean isCRLF(int ch) {
			return ch == '\n' || ch == '\r' || ch == -1;
		}

		private int nextPrintable() {
			try {
				int ch;
				while (!isPrintable(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}

				return ch;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		String next() {
			try {
				int ch = nextPrintable();
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (isPrintable(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		int nextInt() {
			try {
				// parseInt from Integer.parseInt()
				boolean negative = false;
				int res = 0;
				int limit = -Integer.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Integer.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				int multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		long nextLong() {
			try {
				// parseLong from Long.parseLong()
				boolean negative = false;
				long res = 0;
				long limit = -Long.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Long.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				long multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		float nextFloat() {
			return Float.parseFloat(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			try {
				int ch;
				while (isCRLF(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (!isCRLF(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		void close() {
			try {
				br.close();
			} catch (IOException e) {
//				throw new NoSuchElementException();
			}
		}
	}

	private static class Printer extends PrintWriter {
		Printer(OutputStream out) {
			super(out);
		}
	}
}