package contest210709;

import java.io.*;
import java.util.*;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;

public class J {
	InputStream is;
	FastWriter out;

	String INPUT = "";

	public void solve()
	{
		int n = ni(), m = ni();
		int[][] es = new int[m][];
		for(int i = 0;i < m;i++){
			es[i] = new int[]{ni()-1, ni()-1, i};
		}
		final int mod = 100000007;
		DJSet ds = new DJSet(n);
		int[] from = new int[n];
		int[] to = new int[n];
		int[] ws = new int[n];
		boolean[] used = new boolean[m];
		long[] p2 = enumPows(2, n+5, mod);
		int p = 0;
		for(int i = 0;i < m;i++){
			if(!ds.union(es[i][0], es[i][1])){
				from[p] = es[i][0];
				to[p] = es[i][1];
				ws[p] = i+1;
				used[i] = true;
				p++;
			}
		}
		for(int i = 0;i < n;i++){
			if(ds.upper[i] < 0){
				from[p] = i;
				to[p] = n;
				ws[p] = -1;
				p++;
			}
		}
		assert p == n;
		int[][][] g = packWU(n+1, from, to, ws);
		int[][] pars = parents(g, n);
		int[] ord = pars[1], par = pars[0], pw = pars[4], dep = pars[2];
		LCAFast2 lf = LCAFast2.build(packU(n+1, from, to), n);
		HeavyLightDecomposition hld = new HeavyLightDecomposition(packU(n+1, from, to), par, ord, dep);

		LST[] unpainted = new LST[hld.m];
		for(int i = 0;i < hld.m;i++){
			unpainted[i] = new LST(hld.cluspath[i].length);
			unpainted[i].setRange(hld.cluspath[i].length);
		}

		long[] dp = new long[n+1];
		for(int i = 1;i < n+1;i++){
			int cur = ord[i];
			if(par[cur] == n){
				dp[cur] = 0;
			}else{
				dp[cur] = dp[par[cur]] + p2[pw[cur]];
				if(dp[cur] >= mod)dp[cur] -= mod;
			}
		}

		int[] alts = new int[n+1];
		Arrays.fill(alts, -1);

		for(int i = 0;i < m;i++){
			if(!used[i]){
				int f = es[i][0];
				int t = es[i][1];
				int lca = lf.lca(f, t);

				for(int u : new int[]{f, t}) {
					for (int x = u; ; ) {
						int cx = hld.clus[x];
						int l = cx == hld.clus[lca] ? hld.clusiind[lca] : -1;
						int r = hld.clusiind[x];

						while (true) {
							int pr = unpainted[cx].prev(r);
							if (pr != -1 && pr > l) {
								unpainted[cx].unset(pr);
								alts[hld.cluspath[cx][pr]] = i + 1;
							} else {
								break;
							}
						}

						if (cx == hld.clus[lca]) break;
						x = par[hld.cluspath[cx][0]];
					}
				}
			}
		}

		for(int Q = ni();Q > 0;Q--){
			int x = ni()-1, y = ni()-1, z = ni()-1;
			if(!ds.equiv(x, y)){
				out.println(-1);
				continue;
			}
			int lca = lf.lca(x, y);
			boolean hit = false;
			int tar = dep[es[z][0]] > dep[es[z][1]] ? es[z][0] : es[z][1];
			if(used[z]){
				if(dep[x] >= dep[tar] && dep[tar] > dep[lca] && lf.anc(x, dep[x] - dep[tar]) == tar){
					hit = true;
				}
				if(dep[y] >= dep[tar] && dep[tar] > dep[lca] && lf.anc(y, dep[y] - dep[tar]) == tar){
					hit = true;
				}
			}

			long ans = get(x, y, lf, dp);
			if(hit){
				if(alts[tar] == -1){
					out.println(-1);
					continue;
				}

				int s = es[alts[tar]-1][0], t = es[alts[tar]-1][1];
				// x-tar-s?
				boolean pass = false;
				int ll = lf.lca(x, s);
				if(dep[x] >= dep[tar] && dep[tar] > dep[ll] && lf.anc(x, dep[x] - dep[tar]) == tar){
					pass = true;
				}
				if(dep[s] >= dep[tar] && dep[tar] > dep[ll] && lf.anc(s, dep[s] - dep[tar]) == tar){
					pass = true;
				}
				if(pass){
					int d = s; s = t; t = d;
				}

//				tr(x, s, y, t);
				ans = (get(x, s, lf, dp) + get(y, t, lf, dp) + p2[alts[tar]]) % mod;
			}
			out.println(ans);
		}
	}
	final int mod = 1000000007;

	long get(int x, int y, LCAFast2 lf, long[] dp)
	{
		int lca = lf.lca(x, y);
		return (dp[x] + dp[y] - 2*dp[lca] + 2*mod) % mod;
	}

	public static class LST {
		public long[][] set;
		public int n;
		//	public int size;

		public LST(int n) {
			this.n = n;
			int d = 1;
			for(int m = n;m > 1;m>>>=6, d++);

			set = new long[d][];
			for(int i = 0, m = n>>>6;i < d;i++, m>>>=6){
				set[i] = new long[m+1];
			}
			//		size = 0;
		}

		// [0,r)
		public LST setRange(int r)
		{
			for(int i = 0;i < set.length;i++, r=r+63>>>6){
				for(int j = 0;j < r>>>6;j++){
					set[i][j] = -1L;
				}
				if((r&63) != 0)set[i][r>>>6] |= (1L<<r)-1;
			}
			return this;
		}

		// [0,r)
		public LST unsetRange(int r)
		{
			if(r >= 0){
				for(int i = 0;i < set.length;i++, r=r+63>>>6){
					for(int j = 0;j < r+63>>>6;j++){
						set[i][j] = 0;
					}
					if((r&63) != 0)set[i][r>>>6] &= ~((1L<<r)-1);
				}
			}
			return this;
		}

		public LST set(int pos)
		{
			if(pos >= 0 && pos < n){
				//			if(!get(pos))size++;
				for(int i = 0;i < set.length;i++, pos>>>=6){
					set[i][pos>>>6] |= 1L<<pos;
				}
			}
			return this;
		}

		public LST unset(int pos)
		{
			if(pos >= 0 && pos < n){
				//			if(get(pos))size--;
				for(int i = 0;i < set.length && (i == 0 || set[i-1][pos] == 0L);i++, pos>>>=6){
					set[i][pos>>>6] &= ~(1L<<pos);
				}
			}
			return this;
		}

		public boolean get(int pos)
		{
			return pos >= 0 && pos < n && set[0][pos>>>6]<<~pos<0;
		}

		public LST toggle(int pos)
		{
			return get(pos) ? unset(pos) : set(pos);
		}

		public int prev(int pos)
		{
			for(int i = 0;i < set.length && pos >= 0;i++, pos>>>=6, pos--){
				int pre = prev(set[i][pos>>>6], pos&63);
				if(pre != -1){
					pos = pos>>>6<<6|pre;
					while(i > 0)pos = pos<<6|63-Long.numberOfLeadingZeros(set[--i][pos]);
					return pos;
				}
			}
			return -1;
		}

		public int next(int pos)
		{
			for(int i = 0;i < set.length && pos>>>6 < set[i].length;i++, pos>>>=6, pos++){
				int nex = next(set[i][pos>>>6], pos&63);
				if(nex != -1){
					pos = pos>>>6<<6|nex;
					while(i > 0)pos = pos<<6|Long.numberOfTrailingZeros(set[--i][pos]);
					return pos;
				}
			}
			return -1;
		}

		private static int prev(long set, int n)
		{
			long h = set<<~n;
			if(h == 0L)return -1;
			return -Long.numberOfLeadingZeros(h)+n;
		}

		private static int next(long set, int n)
		{
			long h = set>>>n;
			if(h == 0L)return -1;
			return Long.numberOfTrailingZeros(h)+n;
		}

		@Override
		public String toString()
		{
			List<Integer> list = new ArrayList<Integer>();
			for(int pos = next(0);pos != -1;pos = next(pos+1)){
				list.add(pos);
			}
			return list.toString();
		}
	}


	public static class HeavyLightDecomposition {
		public int[][] g;
		public int[] clus;
		public int[][] cluspath;
		public int[] clusiind;
		public int[] par, dep;
		public int m;

		public HeavyLightDecomposition(int[][] g, int[] par, int[] ord, int[] dep) {
			init(g, par, ord, dep);
		}

		public void init(int[][] g, int[] par, int[] ord, int[] dep) {
			clus = decomposeToHeavyLight(g, par, ord);
			cluspath = clusPaths(clus, ord);
			clusiind = clusIInd(cluspath, g.length);
			this.m = cluspath.length;
			this.par = par;
			this.dep = dep;
			this.g = g;
		}

		public static int[] decomposeToHeavyLight(int[][] g, int[] par, int[] ord) {
			int n = g.length;
			int[] size = new int[n];
			Arrays.fill(size, 1);
			for (int i = n - 1; i > 0; i--) size[par[ord[i]]] += size[ord[i]];

			int[] clus = new int[n];
			Arrays.fill(clus, -1);
			int p = 0;
			for (int i = 0; i < n; i++) {
				int u = ord[i];
				if (clus[u] == -1) clus[u] = p++;
				// centroid path (not heavy path)
				int argmax = -1;
				for (int v : g[u]) {
					if (par[u] != v && (argmax == -1 || size[v] > size[argmax])) argmax = v;
				}
				if (argmax != -1) clus[argmax] = clus[u];
			}
			return clus;
		}

		public static int[][] clusPaths(int[] clus, int[] ord) {
			int n = clus.length;
			int[] rp = new int[n];
			int sup = 0;
			for (int i = 0; i < n; i++) {
				rp[clus[i]]++;
				sup = Math.max(sup, clus[i]);
			}
			sup++;

			int[][] row = new int[sup][];
			for (int i = 0; i < sup; i++) row[i] = new int[rp[i]];

			for (int i = n - 1; i >= 0; i--) {
				row[clus[ord[i]]][--rp[clus[ord[i]]]] = ord[i];
			}
			return row;
		}

		public static int[] clusIInd(int[][] clusPath, int n) {
			int[] iind = new int[n];
			for (int[] path : clusPath) {
				for (int i = 0; i < path.length; i++) {
					iind[path[i]] = i;
				}
			}
			return iind;
		}

		public int lca(int x, int y) {
			int rx = cluspath[clus[x]][0];
			int ry = cluspath[clus[y]][0];
			while (clus[x] != clus[y]) {
				if (dep[rx] > dep[ry]) {
					x = par[rx];
					rx = cluspath[clus[x]][0];
				} else {
					y = par[ry];
					ry = cluspath[clus[y]][0];
				}
			}
			return clusiind[x] > clusiind[y] ? y : x;
		}

		public int ancestor(int x, int v) {
			while (x != -1) {
				if (v <= clusiind[x]) return cluspath[clus[x]][clusiind[x] - v];
				v -= clusiind[x] + 1;
				x = par[cluspath[clus[x]][0]];
			}
			return x;
		}

		// [iord[x], right[x])
		public int[][] makeRights() {
			int root = -1;
			int n = g.length;
			for (int i = 0; i < n; i++) if (par[i] == -1) root = i;

			int[] ord = new int[n];
			int[] right = new int[n];

			int[] curs = new int[n];
			int[] inds = new int[n];
			int sp = 0, p = 0;
			curs[sp++] = root;
			while (sp > 0) {
				int cur = curs[sp - 1];
				int ind = inds[sp - 1];
				inds[sp - 1]++;
				if (ind == 0) {
					ord[p++] = cur;
					for (int e : g[cur]) {
						if (par[cur] == e) continue;
						if (clus[cur] == clus[e]) {
							curs[sp] = e;
							inds[sp] = 0;
							sp++;
							break;
						}
					}
				} else if (ind - 1 < g[cur].length) {
					int e = g[cur][ind - 1];
					if (e == par[cur]) continue;
					if (clus[cur] == clus[e]) continue;
					curs[sp] = e;
					inds[sp] = 0;
					sp++;
				} else {
					right[cur] = p;
					sp--;
				}
			}
			int[] iord = new int[n];
			for (int i = 0; i < n; i++) iord[ord[i]] = i;
			return new int[][]{ord, iord, right};
		}

		///// templates


		public void queryNew(int u, int anc, int v) {
			//		for(int x = u;;){
			//			int cx = hld.clus[x];
			//			int l = cx == hld.clus[anc] ? hld.clusiind[anc] : 0;
			//			int r = hld.clusiind[x];
			//
			//			st[cx].add(l, r+1, v); // path query
			//			ans += sumRangeFenwick(ft0, ft1, iord[x]) - sumRangeFenwick(ft0, ft1, iord[hld.cluspath[cx][0]] + l - 1); // subtree query
			//
			//			if(cx == hld.clus[anc])break;
			//			x = par[hld.cluspath[cx][0]];
			//		}
		}

		/**
		 * xとその先祖ancについて経路x-ancでのクエリを処理するテンプレ
		 * @param x
		 * @param anc
		 */
		//	public void query(int x, int anc)
		//	{
		//		int cx = hld.clus[x]; // cluster
		//		int ind = hld.clusiind[x]; // pos in cluster
		//		while(cx != hld.clus[anc]){
		//			// TODO クラスタcxの0~indについて逆向きにクエリ処理
		//			// st[cx].add(0, ind+1, v);
		//			int con = par[hld.cluspath[cx][0]];
		//			ind = hld.clusiind[con];
		//			cx = hld.clus[con];
		//		}
		//		// TODO clusiind[anc]~indについて逆向きにクエリ処理
		//		// st[cx].add(hld.clusiind[anc], ind+1, v);
		//	}
	}


		public static int[][] packU(int n, int[] from, int[] to) {
		return packU(n, from, to, from.length);
	}

	public static int[][] packU(int n, int[] from, int[] to, 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]];
		for (int i = 0; i < sup; i++) {
			g[from[i]][--p[from[i]]] = to[i];
			g[to[i]][--p[to[i]]] = from[i];
		}
		return g;
	}


	public static class LCAFast2 {
		public int n, h;
		public int[][] bigst;
		public int[][] bigind;
		public long[][] smallb;
		public int[] vs, first, deps;

		public int lca(int a, int b)
		{
			return vs[rmqpos(Math.min(first[a], first[b]), Math.max(first[a], first[b]))];
		}

		public int pointOnPath(int a, int b, int dfroma)
		{
			int lca = lca(a, b);
			if(dfroma <= dep(a) - dep(lca)){
				return anc(a, dfroma);
			}
			int dfromb = dep(b) - dep(lca) - (dfroma - (dep(a) - dep(lca)));
			if(dfromb < 0)return -1;

			return anc(b, dfromb);
		}

		public int anc(int a, int d)
		{
			int da = dep(a);
			if(da < d)return -1;
			int danc = da - d;
			int low = 0, high = first[a] + 1;
			while(high - low > 1){
				int h = high+low>>1;
				if(rmqval(h, first[a]) <= danc){
					low = h;
				}else {
					high = h;
				}
			}
			return vs[low];
		}

		public int d(int a, int b)
		{
			return dep(a) + dep(b) - 2 * rmqval(Math.min(first[a], first[b]), Math.max(first[a], first[b]));
		}

		public int dep(int x)
		{
			return deps[first[x]];
		}

		public int rmqpos(int l, int r)
		{
			if(l > r)return -1;
			int cl = l>>>6;
			int cr = r>>>6;
			if(cl == cr){
				return argmax(smallb[l&63][cl], r-l+1) + l;
			}else{
				int min = deps[l] - max(smallb[l&63][cl], 63-(l&63)+1);
				int pos = argmax(smallb[l&63][cl], 63-(l&63)+1) + l;

				{
					int can = deps[r>>>6<<6] - max(smallb[0][cr], (r&63)-0+1);
					if(can < min){
						min = can;
						pos = argmax(smallb[0][cr], (r&63)-0+1) + (r>>>6<<6);
					}
				}

				if(cl+1 <= cr-1){
					int len = (cr-1)-(cl+1)+1;
					int h = 31-Integer.numberOfLeadingZeros(len);
					{
						int can = bigst[h][cl+1];
						if(can < min){
							min = can;
							pos = bigind[h][cl+1];
						}
					}
					{
						int can = bigst[h][cr-1-(1<<h)+1];
						if(can < min){
							min = can;
							pos = bigind[h][cr-1-(1<<h)+1];
						}
					}
				}
				return pos;
			}
		}

		public int rmqval(int l, int r)
		{
			if(l > r)return -1;
			int cl = l>>>6;
			int cr = r>>>6;
			if(cl == cr){
				return deps[l] - max(smallb[l&63][cl], r-l+1);
			}else{
				int min = deps[l] - max(smallb[l&63][cl], 63-(l&63)+1);
				min = Math.min(min, deps[r>>>6<<6] - max(smallb[0][cr], (r&63)-0+1));

				if(cl+1 <= cr-1){
					int len = (cr-1)-(cl+1)+1;
					int h = 31-Integer.numberOfLeadingZeros(len);
					min = Math.min(min, bigst[h][cl+1]);
					min = Math.min(min, bigst[h][cr-1-(1<<h)+1]);
				}
				return min;
			}
		}

		public static LCAFast2 build(int[][] g, int root)
		{
			LCAFast2 ret = new LCAFast2();
			int[][] et = eulerTour(g, root);
			int[] vs = et[0], deps = et[1], first = et[2];
			ret.vs = vs;
			ret.first = first;
			ret.deps = deps;

			int n = deps.length;
			int u = n+63>>>6;
			int h = 31-Integer.numberOfLeadingZeros(u) + 1;
			int[][] bigst = new int[h][];
			int[][] bigind = new int[h][];
			int[] cup = new int[u];
			int[] cupind = new int[u];
			Arrays.fill(cup, Integer.MAX_VALUE);
			for(int i = 0;i < n;i++){
				if(deps[i] < cup[i>>>6]){
					cup[i>>>6] = deps[i];
					cupind[i>>>6] = i;
				}
			}
			bigst[0] = cup;
			bigind[0] = cupind;
			for(int i = 1;i < h;i++){
				bigst[i] = new int[u-(1<<i)+1];
				bigind[i] = new int[u-(1<<i)+1];
				for(int j = 0;j + (1<<i) <= u;j++){
					if(bigst[i-1][j] < bigst[i-1][j+(1<<i-1)]){
						bigst[i][j] = bigst[i-1][j];
						bigind[i][j] = bigind[i-1][j];
					}else{
						bigst[i][j] = bigst[i-1][j+(1<<i-1)];
						bigind[i][j] = bigind[i-1][j+(1<<i-1)];
					}
				}
			}

			long[][] smallb = new long[64][u];
			for(int i = 0;i < u;i++){
				long x = 0;
				for(int j = 0;j < 63 && (i<<6|j+1) < n;j++){
					if(deps[i<<6|j] > deps[i<<6|j+1]){
						x |= 1L<<j;
					}
				}
				long val = 0;
				for(int j = 63;j >= 0;j--){
					val <<= 1;
					if(x<<~j<0){
						val |= 1L;
					}else{
						val &= val - 1;
					}
					smallb[j][i] = val;
				}
				//
				//			for(int j = 0;j < 64;j++){
				//				smallb[j][i] = make(x>>>j);
				//			}
			}

			ret.n = n; ret.h = h;
			ret.bigst = bigst;
			ret.bigind = bigind;
			ret.smallb = smallb;
			return ret;
		}

		public static int[][] eulerTour(int[][] g, int root)
		{
			int n = g.length;
			int[] vs = new int[2*n-1];
			int[] deps = new int[2*n-1];
			int[] first = new int[n];
			Arrays.fill(first, -1);
			int p = 0;

			int[] stack = new int[n];
			int[] inds = new int[n];
			int sp = 0;
			stack[sp++] = root;
			outer:
			while(sp > 0){
				int cur = stack[sp-1], ind = inds[sp-1];
				vs[p] = cur;
				deps[p] = sp-1;
				if(first[cur] == -1)first[cur] = p;
				p++;
				while(ind < g[cur].length){
					int nex = g[cur][ind++];
					if(first[nex] == -1){
						inds[sp-1] = ind;
						stack[sp] = nex;
						inds[sp] = 0;
						sp++;
						continue outer;
					}
				}
				inds[sp-1] = ind;
				if(ind == g[cur].length)sp--;
			}

			return new int[][]{vs, deps, first};
		}

		// TinyRMQ
		public static long make(long x)
		{
			int h = 0;
			int max = 0;
			long ret = 0;
			for(int i = 0;i < 64;i++){
				if(x<<~i<0){
					h++;
				}else{
					h--;
				}
				if(h > max){
					max = h;
					ret |= 1L<<i;
				}
			}
			return ret;
		}

		public static int max(long x, int r)
		{
			assert r > 0;
			return Long.bitCount(x&(1L<<r-1)-1);
		}

		public static int argmax(long x, int r)
		{
			assert r > 0;
			return 64-Long.numberOfLeadingZeros(x&(1L<<r-1)-1);
		}

	}


	public static long[] enumPows(int a, int n, int mod)
	{
		a %= mod;
		long[] pows = new long[n+1];
		pows[0] = 1;
		for(int i = 1;i <= n;i++)pows[i] = pows[i-1] * a % mod;
		return pows;
	}


	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 int[][] parents(int[][][] g, int root) {
		int n = g.length;
		int[] par = new int[n];
		Arrays.fill(par, -1);
		int[] dw = new int[n];
		int[] pw = new int[n];
		int[] dep = new int[n];

		int[] q = new int[n];
		q[0] = root;
		for (int p = 0, r = 1; p < r; p++) {
			int cur = q[p];
			for (int[] nex : g[cur]) {
				if (par[cur] != nex[0]) {
					q[r++] = nex[0];
					par[nex[0]] = cur;
					dep[nex[0]] = dep[cur] + 1;
					dw[nex[0]] = dw[cur] + nex[1];
					pw[nex[0]] = nex[1];
				}
			}
		}
		return new int[][]{par, q, dep, dw, pw};
	}


	public static class DJSet {
		public int[] upper;

		public DJSet(int n) {
			upper = new int[n];
			Arrays.fill(upper, -1);
		}

		public int root(int x) {
			return upper[x] < 0 ? x : (upper[x] = root(upper[x]));
		}

		public boolean equiv(int x, int y) {
			return root(x) == root(y);
		}

		public boolean union(int x, int y) {
			x = root(x);
			y = root(y);
			if (x != y) {
				if (upper[y] < upper[x]) {
					int d = x;
					x = y;
					y = d;
				}
				upper[x] += upper[y];
				upper[y] = x;
			}
			return x == y;
		}

		public int count() {
			int ct = 0;
			for (int u : upper) if (u < 0) ct++;
			return ct;
		}

		public int[][] toBucket() {
			int n = upper.length;
			int[][] ret = new int[n][];
			int[] rp = new int[n];
			for (int i = 0; i < n; i++) if (upper[i] < 0) ret[i] = new int[-upper[i]];
			for (int i = 0; i < n; i++) {
				int r = root(i);
				ret[r][rp[r]++] = i;
			}
			return ret;
		}
	}


	public static void main(String[] args) {
		new J().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[] 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<Integer> 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)); }
}