Problem: The Prodiggers are quite a cool band and for this reason, they have been the surprise guest at the ENTER festival for the past 80 years. At the beginning of their careers, they weren’t so successful, so they had to spend time digging channels to earn money; hence the name. Anyway, they like to tour a lot and have surprising amounts of energy to do extremely long tours. However, they hate spending two consecutive days without having a concert, so they would like to avoid it.

A tour is defined by a sequence of concerts and days-off. You need to count in how many ways The Prodiggers can select k different tours of the same length between l and r.

For example if k = 2, l = 1 and r = 2, if we define concert day as {1} and day-off as {0}, here are all possible tours: {0}, {1}, {00}, {01}, {10}, {11}. But tour 00 can not be selected because it has 2 days-off in a row. Now, we need to count in how many ways we can select k = 2 tours of the same length in range [1;2]. Here they are: {0,1}; {01,10}; {01,11}; {10,11}.

Since their schedule is quite busy, they want you to tell them in how many ways can do that, modulo 1 000 000 007 (109 + 7).

Input

The first line of the input contains three integers k, l and r (1 ≤ k ≤ 200, 1 ≤ l ≤ r ≤ 1018).

Output

Output a single number: the number of ways to select k different tours of the same length, modulo 1 000 000 007.

Example

Input

1 1 2


Output

5

Solution (in JAVA):

Solution:
//package bubblecup9f;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class A5 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	final int mod = 1000000007;
	
	public static int[][] enumFIF(int n, int mod) {
		int[] f = new int[n + 1];
		int[] invf = new int[n + 1];
		f[0] = 1;
		for (int i = 1; i <= n; i++) {
			f[i] = (int) ((long) f[i - 1] * i % mod);
		}
		long a = f[n];
		long b = mod;
		long p = 1, q = 0;
		while (b > 0) {
			long c = a / b;
			long d;
			d = a;
			a = b;
			b = d % b;
			d = p;
			p = q;
			q = d - c * q;
		}
		invf[n] = (int) (p < 0 ? p + mod : p);
		for (int i = n - 1; i >= 0; i--) {
			invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod);
		}
		return new int[][] { f, invf };
	}

	
	void solve()
	{
		int K = ni();
		long L = nl(), R = nl();
		
		int[][] fif = enumFIF(K+2, mod);
		
		long[][] fs = new long[K+1][K+1];
		fs[0][0] = fif[1][K];
		for(int i = 0;i < K;i++){
			for(int j = 0;j <= i;j++){
				fs[i+1][j+1] += fs[i][j];
				if(fs[i+1][j+1] >= mod)fs[i+1][j+1] -= mod;
				fs[i+1][j] += fs[i][j] * (mod-i);
				fs[i+1][j] %= mod;
			}
		}
		
		long ret = count(R+1, fs[K], fif) - count(L, fs[K], fif);
		if(ret < 0)ret += mod;
		out.println(ret);
	}
	
	long count(long n, long[] fs, int[][] fif)
	{
		long ret = 0;
		for(int i = 0;i < fs.length;i++){
			ret += fpowsum(i, n, mod, fif) * fs[i];
			ret %= mod;
		}
		return ret;
	}
	
	long fpowsum(int K, long n, int mod, int[][] fif)
	{
		Exmod plus = Exmod.div(new Exmod(1,1),2);
		Exmod[] pluss = new Exmod[K+1];
		pluss[0] = new Exmod(1);
		for(int i = 1;i <= K;i++)pluss[i] = Exmod.mul(pluss[i-1], plus);
		
		Exmod minus = Exmod.div(new Exmod(1,-1),2);
		Exmod[] minuss = new Exmod[K+1];
		minuss[0] = new Exmod(1);
		for(int i = 1;i <= K;i++)minuss[i] = Exmod.mul(minuss[i-1], minus);
		
		Exmod ret = new Exmod(0);
		for(int i = K, sig = 1;i >= 0;i--, sig = -sig){
			Exmod ratio = Exmod.mul(pluss[i], minuss[K-i]);
			ret.add(Exmod.mul(Exmod.sumgp(ratio, n+2), C(K, i, mod, fif) * sig));
		}
		
		Exmod fifth = Exmod.pow(Exmod.inv(new Exmod(0, 1)), K);
		ret.mul(fifth);
		
		assert ret.b == 0;
		return ret.a;
	}
	
	public static long C(int n, int r, int mod, int[][] fif) {
		if (n < 0 || r < 0 || r > n)
			return 0;
		return (long) fif[0][n] * fif[1][r] % mod * fif[1][n - r] % mod;
	}
	
	public static class Exmod {
		public long a, b;
		public static final long E = 5;
		public static final int mod = 1000000007;
		
		@Override
		public String toString() {
			if(a == 0 && b == 0)return "0";
			StringBuilder ret = new StringBuilder();
			if(a != 0){
				ret.append(a);
				if(b > 0)ret.append("+");
			}
			if(b != 0)ret.append(b + "√" + E);
			return ret.toString();
		}

		public Exmod(long a) {
			this.a = a;
			this.b = 0;
			normalize();
		}
		
		public Exmod(long a, long b) {
			this.a = a;
			this.b = b;
			normalize();
		}
		
		public Exmod(Exmod e) {
			this.a = e.a;
			this.b = e.b;
			normalize();
		}
		
		public void normalize(){
			if(a >= mod || a < 0){
				a %= mod;
				if(a < 0)a += mod;
			}
			if(b >= mod || b < 0){
				b %= mod;
				if(b < 0)b += mod;
			}
		}
		
		public Exmod add(Exmod t){ a += t.a; b += t.b; normalize(); return this; }
		public Exmod sub(Exmod t){ a -= t.a; b -= t.b; normalize(); return this; }
		public Exmod mul(Exmod t){
			long na = a * t.a + b * t.b * E;
			long nb = a * t.b + b * t.a;
			a = na; b = nb; normalize(); return this;
		}
		public Exmod div(Exmod t){
			long den = t.a*t.a-E*t.b*t.b;
			den %= mod; if(den < 0)den += mod;
			long iden = invl(den, mod);
			long numr = (a*t.a - b*t.b*E) % mod * iden % mod;
			long numi = (b*t.a - a*t.b) % mod * iden % mod;
			a = numr; b = numi; normalize(); return this;
		}
		public Exmod negate(){ a = -a; b = -b; normalize(); return this; }

		public static Exmod negate(Exmod a){ return new Exmod(-a.a, -a.b);}
		public static Exmod add(Exmod a, Exmod b){return new Exmod(a.a + b.a, a.b + b.b);}
		public static Exmod sub(Exmod a, Exmod b){return new Exmod(a.a - b.a, a.b - b.b);}
		public static Exmod mul(Exmod a, Exmod b){return new Exmod(a.a * b.a + a.b * b.b * E, a.a * b.b + a.b * b.a);}
		public static Exmod div(Exmod a, Exmod b){
			long den = b.a*b.a-E*b.b*b.b;
			den %= mod; if(den < 0)den += mod;
			long iden = invl(den, mod);
			long numr = (a.a*b.a - a.b*b.b*E) % mod * iden % mod;
			if(numr < 0)numr += mod;
			long numi = (a.b*b.a - a.a*b.b) % mod * iden % mod;
			if(numi < 0)numi += mod;
			return new Exmod(numr, numi);
		}
		
		public static Exmod inv(Exmod a){
			long den = a.a*a.a-E*a.b*a.b;
			den %= mod; if(den < 0)den += mod;
			long iden = invl(den, mod);
			long numr = a.a * iden % mod;
			long numi = -a.b * iden % mod;
			if(numi < 0)numi += mod;
			return new Exmod(numr, numi);
		}
		
		// a+bx (a+bx)(c-dx) (ac-bdE)+x(bc-ad)
		// ----=------------=-----------------
		// c+dx (c+dx)(c-dx)    c^2-Ed^2
		
		public static Exmod mul(Exmod a, long b){return new Exmod(a.a * b, a.b * b);}
		public static Exmod div(Exmod a, long b){return mul(a, invl(b, mod));}
		
		public static Exmod pow(Exmod a, long n) {
			Exmod ret = new Exmod(1);
			int x = 63 - Long.numberOfLeadingZeros(n);
			for (; x >= 0; x--) {
				ret = mul(ret, ret);
				if(n<<~x<0)ret = mul(ret, a);
			}
			return ret;
		}
		
		public static Exmod sumgp(Exmod a, long n)
		{
			Exmod mul = new Exmod(1);
			Exmod ret = new Exmod(0);
			for(int i = 63-Long.numberOfLeadingZeros(n);i >= 0;i--){
				mul.a += 1;
				ret = mul(ret, mul);
				mul.a -= 1;
				mul = mul(mul, mul);
				if(n<<~i<0){
					ret = mul(ret, a);
					ret.a++; ret.normalize();
					mul = mul(mul, a);
				}
			}
			return ret;
		}
		
		public static long invl(long a, long mod) {
			long b = mod;
			long p = 1, q = 0;
			while (b > 0) {
				long c = a / b;
				long d;
				d = a;
				a = b;
				b = d % b;
				d = p;
				p = q;
				q = d - c * q;
			}
			return p < 0 ? p + mod : p;
		}
	}

	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new A5().run(); }
	
	private byte[] inbuf = new byte[1024];
	private 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 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))){ // when nextLine, (isSpaceChar(b) && 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 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();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}