package contest240517; import java.io.*; import java.util.ArrayDeque; import java.util.Arrays; import java.util.InputMismatchException; import java.util.Queue; import java.util.function.IntUnaryOperator; import java.util.function.LongUnaryOperator; public class H { InputStream is; FastWriter out; String INPUT = ""; public void solve() { int n = ni(), m = ni(); int[] w = na(n); int[] from = new int[m]; int[] to = new int[m]; long[] ws = new long[m]; for(int i = 0;i < m;i++){ from[i] = ni()-1; to[i] = ni()-1; ws[i] = nl(); } GraphW g = packWU(n, from, to, ws); long[] ds = dijk(n, 0, g); LiChaoTree lct = new LiChaoTree(0, 40); for(int i = 0;i < n;i++){ lct.add(w[i], ds[i]); } long[] ne = new long[n]; for(int i = 0;i < n;i++){ ne[i] = Math.min(ds[i], lct.f(w[i])); } long[] dt = dijk(n, ne, g); out.println(dt[n-1]); } long[] dijk(int n, int from, GraphW g){ long[] td = new long[n]; Arrays.fill(td, Long.MAX_VALUE / 2); MinHeapL q = new MinHeapL(n); q.add(0, 0); td[0] = 0; while(q.size() > 0){ int cur = q.argmin(); q.remove(cur); for(int i = 0;i < g.g[cur].length;i++){ int e = g.g[cur][i]; long nd = td[cur] + g.wg[cur][i]; if(nd < td[e]){ td[e] = nd; q.update(e, nd); } } } return td; } long[] dijk(int n, long[] td, GraphW g){ MinHeapL q = new MinHeapL(n); for(int i = 0;i < n;i++){ q.add(i, td[i]); } while(q.size() > 0){ int cur = q.argmin(); q.remove(cur); for(int i = 0;i < g.g[cur].length;i++){ int e = g.g[cur][i]; long nd = td[cur] + g.wg[cur][i]; if(nd < td[e]){ td[e] = nd; q.update(e, nd); } } } return td; } public static class LiChaoTree { public LL as; public LL bs; public long L; public int D; public L lefts, rights; // [L, L+(1<= cr)return -1; if(l <= cl && cr <= r){ if(cur == -1){ as.add(a); bs.add(b); lefts.add(-1); rights.add(-1); return as.p-1; } boolean lessl = f(cl, a, b) < f(cl, as.a[cur], bs.a[cur]); boolean lessr = f(cr-1, a, b) < f(cr-1, as.a[cur], bs.a[cur]); if(!lessl && !lessr){ // not need to append return cur; } if(lessl && lessr){ // replace current as.a[cur] = a; bs.a[cur] = b; return cur; } long cm = cl + (cr-cl)/2; boolean lessm = f(cm, a, b) < f(cm, as.a[cur], bs.a[cur]); if(lessm){ {long d = as.a[cur]; as.a[cur] = a; a = d;} {long d = bs.a[cur]; bs.a[cur] = b; b = d;} lessl = !lessl; lessr = !lessr; } if(lessl){ int res = add(a, b, lefts.a[cur], l, r, cl, cm); lefts.a[cur] = res; }else{ int res = add(a, b, rights.a[cur], l, r, cm, cr); rights.a[cur] = res; } return cur; } long cm = cl + (cr-cl)/2; if(cur == -1){ as.add(0); bs.add(Long.MAX_VALUE); lefts.add(-1); rights.add(-1); cur = as.p-1; } if(l < cm){ int res = add(a, b, lefts.a[cur], l, r, cl, cm); lefts.a[cur] = res; } if(cm < r){ int res = add(a, b, rights.a[cur], l, r, cm, cr); rights.a[cur] = res; } return cur; } public long f(long x) { assert L <= x; assert x < L+(1L<= 0 && cur != -1;m--){ min = Math.min(min, f(x, as.a[cur], bs.a[cur])); cur = x-L<< -m <0 ? rights.a[cur] : lefts.a[cur]; } return min; } public static class L { public int[] a; public int p = 0; public L(int n) { a = new int[n]; } public L add(int n) { if(p >= a.length)a = Arrays.copyOf(a, a.length*3/2+1); a[p++] = n; return this; } public int size() { return p; } public L clear() { p = 0; return this; } public int[] toArray() { return Arrays.copyOf(a, p); } @Override public String toString() {return Arrays.toString(toArray());} } public static class LL { public long[] a; public int p = 0; public LL(int n) { a = new long[n]; } public LL add(long n) { if(p >= a.length)a = Arrays.copyOf(a, a.length*3/2+1); a[p++] = n; return this; } public int size() { return p; } public LL clear() { p = 0; return this; } public long[] toArray() { return Arrays.copyOf(a, p); } @Override public String toString() {return Arrays.toString(toArray());} } } public static class MinHeapL { public long[] a; public int[] map; public int[] imap; public int n; public int pos; public static long INF = Long.MAX_VALUE; public MinHeapL(int m) { n = Integer.highestOneBit((m+1)<<1); a = new long[n]; map = new int[n]; imap = new int[n]; Arrays.fill(a, INF); Arrays.fill(map, -1); Arrays.fill(imap, -1); pos = 1; } public long add(int ind, long x) { int ret = imap[ind]; if(imap[ind] < 0){ a[pos] = x; map[pos] = ind; imap[ind] = pos; pos++; up(pos-1); } return ret != -1 ? a[ret] : x; } public long update(int ind, long x) { int ret = imap[ind]; if(imap[ind] < 0){ a[pos] = x; map[pos] = ind; imap[ind] = pos; pos++; up(pos-1); }else{ a[ret] = x; up(ret); down(ret); } return x; } public long remove(int ind) { if(pos == 1)return INF; if(imap[ind] == -1)return INF; pos--; int rem = imap[ind]; long ret = a[rem]; map[rem] = map[pos]; imap[map[pos]] = rem; imap[ind] = -1; a[rem] = a[pos]; a[pos] = INF; map[pos] = -1; up(rem); down(rem); return ret; } public long min() { return a[1]; } public int argmin() { return map[1]; } public int size() { return pos-1; } private void up(int cur) { for(int c = cur, p = c>>>1;p >= 1 && a[p] > a[c];c>>>=1, p>>>=1){ long d = a[p]; a[p] = a[c]; a[c] = d; int e = imap[map[p]]; imap[map[p]] = imap[map[c]]; imap[map[c]] = e; e = map[p]; map[p] = map[c]; map[c] = e; } } private void down(int cur) { for(int c = cur;2*c < pos;){ int b = a[2*c] < a[2*c+1] ? 2*c : 2*c+1; if(a[b] < a[c]){ long d = a[c]; a[c] = a[b]; a[b] = d; int e = imap[map[c]]; imap[map[c]] = imap[map[b]]; imap[map[b]] = e; e = map[c]; map[c] = map[b]; map[b] = e; c = b; }else{ break; } } } } public static GraphW packWU(int n, int[] from, int[] to, long[] w) { int[][] g = new int[n][]; long[][] wg = new long[n][]; int[] p = new int[n]; for(int f : from)p[f]++; for(int t : to)p[t]++; for(int i = 0;i < n;i++){ g[i] = new int[p[i]]; wg[i] = new long[p[i]]; } for(int i = 0;i < from.length;i++){ --p[from[i]]; g[from[i]][p[from[i]]] = to[i]; wg[from[i]][p[from[i]]] = w[i]; --p[to[i]]; g[to[i]][p[to[i]]] = from[i]; wg[to[i]][p[to[i]]] = w[i]; } GraphW gw = new GraphW(); gw.g = g; gw.wg = wg; return gw; } public static class GraphW { public int[][] g; public long[][] wg; } public static int[][][] packWU(int n, int[] from, int[] to, int[] w) { return packWU(n, from, to, w, from.length); } public static int[][][] packWU(int n, int[] from, int[] to, int[] w, int sup) { int[][][] g = new int[n][][]; int[] p = new int[n]; for (int i = 0; i < sup; i++) p[from[i]]++; for (int i = 0; i < sup; i++) p[to[i]]++; for (int i = 0; i < n; i++) g[i] = new int[p[i]][2]; for (int i = 0; i < sup; i++) { --p[from[i]]; g[from[i]][p[from[i]]][0] = to[i]; g[from[i]][p[from[i]]][1] = w[i]; --p[to[i]]; g[to[i]][p[to[i]]][0] = from[i]; g[to[i]][p[to[i]]][1] = w[i]; } return g; } public static void main(String[] args) { new H().run(); } public void run() { long S = System.currentTimeMillis(); is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new FastWriter(System.out); solve(); out.flush(); long G = System.currentTimeMillis(); tr(G-S+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } private boolean eof() { if(lenbuf == -1)return true; int lptr = ptrbuf; while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false; try { is.mark(1000); while(true){ int b = is.read(); if(b == -1){ is.reset(); return true; }else if(!isSpaceChar(b)){ is.reset(); return false; } } } catch (IOException e) { return true; } } private final byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } // private boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[][] nmi(int n, int m) { int[][] map = new int[n][]; for(int i = 0;i < n;i++)map[i] = na(m); return map; } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } private int ni() { int num = 0, b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } public static class FastWriter { private static final int BUF_SIZE = 1<<13; private final byte[] buf = new byte[BUF_SIZE]; private final OutputStream out; private int ptr = 0; private FastWriter(){out = null;} public FastWriter(OutputStream os) { this.out = os; } public FastWriter(String path) { try { this.out = new FileOutputStream(path); } catch (FileNotFoundException e) { throw new RuntimeException("FastWriter"); } } public FastWriter write(byte b) { buf[ptr++] = b; if(ptr == BUF_SIZE)innerflush(); return this; } public FastWriter write(char c) { return write((byte)c); } public FastWriter write(char[] s) { for(char c : s){ buf[ptr++] = (byte)c; if(ptr == BUF_SIZE)innerflush(); } return this; } public FastWriter write(String s) { s.chars().forEach(c -> { buf[ptr++] = (byte)c; if(ptr == BUF_SIZE)innerflush(); }); return this; } private static int countDigits(int l) { if (l >= 1000000000) return 10; if (l >= 100000000) return 9; if (l >= 10000000) return 8; if (l >= 1000000) return 7; if (l >= 100000) return 6; if (l >= 10000) return 5; if (l >= 1000) return 4; if (l >= 100) return 3; if (l >= 10) return 2; return 1; } public FastWriter write(int x) { if(x == Integer.MIN_VALUE){ return write((long)x); } if(ptr + 12 >= BUF_SIZE)innerflush(); if(x < 0){ write((byte)'-'); x = -x; } int d = countDigits(x); for(int i = ptr + d - 1;i >= ptr;i--){ buf[i] = (byte)('0'+x%10); x /= 10; } ptr += d; return this; } private static int countDigits(long l) { if (l >= 1000000000000000000L) return 19; if (l >= 100000000000000000L) return 18; if (l >= 10000000000000000L) return 17; if (l >= 1000000000000000L) return 16; if (l >= 100000000000000L) return 15; if (l >= 10000000000000L) return 14; if (l >= 1000000000000L) return 13; if (l >= 100000000000L) return 12; if (l >= 10000000000L) return 11; if (l >= 1000000000L) return 10; if (l >= 100000000L) return 9; if (l >= 10000000L) return 8; if (l >= 1000000L) return 7; if (l >= 100000L) return 6; if (l >= 10000L) return 5; if (l >= 1000L) return 4; if (l >= 100L) return 3; if (l >= 10L) return 2; return 1; } public FastWriter write(long x) { if(x == Long.MIN_VALUE){ return write("" + x); } if(ptr + 21 >= BUF_SIZE)innerflush(); if(x < 0){ write((byte)'-'); x = -x; } int d = countDigits(x); for(int i = ptr + d - 1;i >= ptr;i--){ buf[i] = (byte)('0'+x%10); x /= 10; } ptr += d; return this; } public FastWriter write(double x, int precision) { if(x < 0){ write('-'); x = -x; } x += Math.pow(10, -precision)/2; // if(x < 0){ x = 0; } write((long)x).write("."); x -= (long)x; for(int i = 0;i < precision;i++){ x *= 10; write((char)('0'+(int)x)); x -= (int)x; } return this; } public FastWriter writeln(char c){ return write(c).writeln(); } public FastWriter writeln(int x){ return write(x).writeln(); } public FastWriter writeln(long x){ return write(x).writeln(); } public FastWriter writeln(double x, int precision){ return write(x, precision).writeln(); } public FastWriter write(int... xs) { boolean first = true; for(int x : xs) { if (!first) write(' '); first = false; write(x); } return this; } public FastWriter write(long... xs) { boolean first = true; for(long x : xs) { if (!first) write(' '); first = false; write(x); } return this; } public FastWriter write(IntUnaryOperator f, int... xs) { boolean first = true; for(int x : xs) { if (!first) write(' '); first = false; write(f.applyAsInt(x)); } return this; } public FastWriter write(LongUnaryOperator f, long... xs) { boolean first = true; for(long x : xs) { if (!first) write(' '); first = false; write(f.applyAsLong(x)); } return this; } public FastWriter writeln() { return write((byte)'\n'); } public FastWriter writeln(int... xs) { return write(xs).writeln(); } public FastWriter writeln(long... xs) { return write(xs).writeln(); } public FastWriter writeln(IntUnaryOperator f, int... xs) { return write(f, xs).writeln(); } public FastWriter writeln(LongUnaryOperator f, long... xs) { return write(f, xs).writeln(); } public FastWriter writeln(char[] line) { return write(line).writeln(); } public FastWriter writeln(char[]... map) { for(char[] line : map)write(line).writeln();return this; } public FastWriter writeln(String s) { return write(s).writeln(); } private void innerflush() { try { out.write(buf, 0, ptr); ptr = 0; } catch (IOException e) { throw new RuntimeException("innerflush"); } } public void flush() { innerflush(); try { out.flush(); } catch (IOException e) { throw new RuntimeException("flush"); } } public FastWriter print(byte b) { return write(b); } public FastWriter print(char c) { return write(c); } public FastWriter print(char[] s) { return write(s); } public FastWriter print(String s) { return write(s); } public FastWriter print(int x) { return write(x); } public FastWriter print(long x) { return write(x); } public FastWriter print(double x, int precision) { return write(x, precision); } public FastWriter println(char c){ return writeln(c); } public FastWriter println(int x){ return writeln(x); } public FastWriter println(long x){ return writeln(x); } public FastWriter println(double x, int precision){ return writeln(x, precision); } public FastWriter print(int... xs) { return write(xs); } public FastWriter print(long... xs) { return write(xs); } public FastWriter print(IntUnaryOperator f, int... xs) { return write(f, xs); } public FastWriter print(LongUnaryOperator f, long... xs) { return write(f, xs); } public FastWriter println(int... xs) { return writeln(xs); } public FastWriter println(long... xs) { return writeln(xs); } public FastWriter println(IntUnaryOperator f, int... xs) { return writeln(f, xs); } public FastWriter println(LongUnaryOperator f, long... xs) { return writeln(f, xs); } public FastWriter println(char[] line) { return writeln(line); } public FastWriter println(char[]... map) { return writeln(map); } public FastWriter println(String s) { return writeln(s); } public FastWriter println() { return writeln(); } } public static void trnz(int... o) { for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" "); System.out.println(); } // print ids which are 1 public static void trt(long... o) { Queue stands = new ArrayDeque<>(); for(int i = 0;i < o.length;i++){ for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x)); } System.out.println(stands); } public static void tf(boolean... r) { for(boolean x : r)System.out.print(x?'#':'.'); System.out.println(); } public static void tf(boolean[]... b) { for(boolean[] r : b) { for(boolean x : r)System.out.print(x?'#':'.'); System.out.println(); } System.out.println(); } public void tf(long[]... b) { if(INPUT.length() != 0) { for (long[] r : b) { for (long x : r) { for (int i = 0; i < 64; i++) { System.out.print(x << ~i < 0 ? '#' : '.'); } } System.out.println(); } System.out.println(); } } public void tf(long... b) { if(INPUT.length() != 0) { for (long x : b) { for (int i = 0; i < 64; i++) { System.out.print(x << ~i < 0 ? '#' : '.'); } } System.out.println(); } } private void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); } }