CF_372_B.java

import java.io.*;
import java.math.*;
import java.util.*;

import static java.util.Arrays.*;

public class B {
	private static final int mod = (int)1e9+7;

	final Random random = new Random(0);
	final IOFast io = new IOFast();

	/// MAIN CODE
	public void run() throws IOException {
//		int TEST_CASE = Integer.parseInt(new String(io.nextLine()).trim());
		int TEST_CASE = 1;
		while(TEST_CASE-- != 0) {
			int n = io.nextInt();
			int m = io.nextInt();
			int L = io.nextInt();
			int s = io.nextInt();
			int t = io.nextInt();
			
			List<int[]> es2 = new ArrayList<>();
			long[][] es = new long[m][];
			int[] es3 = new int[m];
			WeightedAdjListGraph g = new WeightedAdjListGraph(n, 2*m);
			for(int i = 0; i < m; i++) {
				int a = io.nextInt();
				int b = io.nextInt();
				long c = io.nextInt();
				es[i] = new long[]{a,b,c,};
				int x = g.addEdge(a, b, c);
				int y = g.addEdge(b, a, c);
				es3[i] = x;
				if(c == 0) {
					es2.add(new int[]{x, y});
				}
			}
			long low = 0, high = 1L<<62;
			while(high - low > 1) {
				long mid = (low + high) / 2;
				long rest = mid;
				for(int[] e : es2) {
					long v = Math.max(1, Math.min(rest, 1L<<32));
					g.cost[e[0]] = g.cost[e[1]] = v;
					rest -= v;
				}
				long d = g.dijkstra(s)[0][t];
				if(d < L) {
					low = mid;
				} else if(d > L) {
					high = mid;
				} else {
					io.out.println("YES");
					for(int i = 0; i < m; i++) {
						io.out.println(es[i][0] + " " + es[i][1] + " " + g.cost[es3[i]]);
					}
					return;
				}
			}
			io.out.println("NO");
		}
	}

	static
	class WeightedAdjListGraph {
		int m, V, E;
		int[] head, next, to;
		long[] cost;

		public WeightedAdjListGraph(int V, int E) {
			head = new int[V];
			next = new int[E];
			cost = new long[E];
			to = new int[E];
			this.V = V;
			this.E = E;
			clear();
		}

		public void clear() {
			m = 0;
			Arrays.fill(head, -1);
		}

		public int addEdge(int s, int t, long c) {
			next[m] = head[s];
			cost[m] = c;
			head[s] = m;
			to[m++] = t;
			return m - 1;
		}

		static final PriorityQueue<long[]> q = new PriorityQueue<long[]>(10, new Comparator<long[]>() {
			@Override
			public int compare(long[] o1, long[] o2) {
				return Long.compare(o1[0], o2[0]);
			}
		});

		public long[][] dijkstra(final int s) {
			final long[] dist = new long[head.length];
			final long[] prev = new long[head.length];
			Arrays.fill(dist, -1L);
			Arrays.fill(prev, -1L);
			dist[s] = 0;
			q.add(new long[] { 0, s, });
			while(!q.isEmpty()) {
				final long[] xs = q.poll();
				final int v = (int)xs[1];
				final long d = xs[0];
				if(dist[v] < d) continue;
				
				for(int e = head[v]; e != -1; e = next[e]) {
					final int t = to[e];
					final long w = d + cost[e];
					if(dist[t] < 0 || w < dist[t]) {
						dist[t] = w;
						prev[t] = v;
						q.add(new long[] { w, t, });
					}
				}
			}
			return new long[][]{dist,prev};
		}
		
		/*
		public long[] update(final long[] dist, final int s, final long d0) {
			if(dist[s] != -1 && dist[s] < d0) {
				return dist;
			}
			
			dist[s] = d0;
			q.add(new long[] { d0, s, });
			while(!q.isEmpty()) {
				final long[] xs = q.poll();
				final int v = (int)xs[1];
				final long d = xs[0];
				if(dist[v] < d) continue;
				
				for(int e = head[v]; e != -1; e = next[e]) {
					final int t = to[e];
					final long w = d + cost[e];
					if(dist[t] < 0 || w < dist[t]) {
						dist[t] = w;
						q.add(new long[] { w, t, });
					}
				}
			}
			return dist;
		}
		
		public long[] dijkstra(final int s) {
			final long[] dist = new long[head.length];
			Arrays.fill(dist, -1L);
			return update(dist, s, 0);
		}
		*/
	}

	/// TEMPLATE
	static int gcd(int n, int r) { return r == 0 ? n : gcd(r, n%r); }
	static long gcd(long n, long r) { return r == 0 ? n : gcd(r, n%r); }
	
	static <T> void swap(T[] x, int i, int j) { T t = x[i]; x[i] = x[j]; x[j] = t; }
	static void swap(int[] x, int i, int j) { int t = x[i]; x[i] = x[j]; x[j] = t; }

	void printArrayLn(int[] xs) { for(int i = 0; i < xs.length; i++) io.out.print(xs[i] + (i==xs.length-1?"\n":" ")); }
	void printArrayLn(long[] xs) { for(int i = 0; i < xs.length; i++) io.out.print(xs[i] + (i==xs.length-1?"\n":" ")); }
	
	static void dump(Object... o) { System.err.println(Arrays.deepToString(o)); } 
	
	void main() throws IOException {
		//		IOFast.setFileIO("rle-size.in", "rle-size.out");
		try { run(); }
		catch (EndOfFileRuntimeException e) { }
		io.out.flush();
	}
	public static void main(String[] args) throws IOException { new B().main(); }
	
	static class EndOfFileRuntimeException extends RuntimeException {
		private static final long serialVersionUID = -8565341110209207657L; }

	static
	public class IOFast {
		private BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		private PrintWriter out = new PrintWriter(System.out);

		void setFileIn(String ins) throws IOException { in.close(); in = new BufferedReader(new FileReader(ins)); }
		void setFileOut(String outs) throws IOException { out.flush(); out.close(); out = new PrintWriter(new FileWriter(outs)); }
		void setFileIO(String ins, String outs) throws IOException { setFileIn(ins); setFileOut(outs); }

		private static int pos, readLen;
		private static final char[] buffer = new char[1024 * 8];
		private static char[] str = new char[500*8*2];
		private static boolean[] isDigit = new boolean[256];
		private static boolean[] isSpace = new boolean[256];
		private static boolean[] isLineSep = new boolean[256];

		static { for(int i = 0; i < 10; i++) { isDigit['0' + i] = true; } isDigit['-'] = true; isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true; isLineSep['\r'] = isLineSep['\n'] = true; }
		public int read() throws IOException { if(pos >= readLen) { pos = 0; readLen = in.read(buffer); if(readLen <= 0) { throw new EndOfFileRuntimeException(); } } return buffer[pos++]; }
		public int nextInt() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; int ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; }
		public long nextLong() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; long ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; }
		public char nextChar() throws IOException { while(true) { final int c = read(); if(!isSpace[c]) { return (char)c; } } }
		int reads(int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } if(str.length == len) { char[] rep = new char[str.length * 3 / 2]; System.arraycopy(str, 0, rep, 0, str.length); str = rep; } str[len++] = (char)c; } } catch(EndOfFileRuntimeException e) { ; } return len; }
		int reads(char[] cs, int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } cs[len++] = (char)c; } } catch(EndOfFileRuntimeException e) { ; } return len; }
		public char[] nextLine() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isLineSep); try { if(str[len-1] == '\r') { len--; read(); } } catch(EndOfFileRuntimeException e) { ; } return Arrays.copyOf(str, len); }
		public String nextString() throws IOException { return new String(next()); }
		public char[] next() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); return Arrays.copyOf(str, len); }
//		public int next(char[] cs) throws IOException { int len = 0; cs[len++] = nextChar(); len = reads(cs, len, isSpace); return len; }
		public double nextDouble() throws IOException { return Double.parseDouble(nextString()); }
		public long[] nextLongArray(final int n) throws IOException { final long[] res = new long[n]; for(int i = 0; i < n; i++) { res[i] = nextLong(); } return res; }
		public int[] nextIntArray(final int n) throws IOException { final int[] res = new int[n]; for(int i = 0; i < n; i++) { res[i] = nextInt(); } return res; }
		public int[][] nextIntArray2D(final int n, final int k) throws IOException { final int[][] res = new int[n][]; for(int i = 0; i < n; i++) { res[i] = nextIntArray(k); } return res; }
		public int[][] nextIntArray2DWithIndex(final int n, final int k) throws IOException { final int[][] res = new int[n][k+1]; for(int i = 0; i < n; i++) { for(int j = 0; j < k; j++) { res[i][j] = nextInt(); } res[i][k] = i; } return res; }
		public double[] nextDoubleArray(final int n) throws IOException { final double[] res = new double[n]; for(int i = 0; i < n; i++) { res[i] = nextDouble(); } return res; }
	}
}