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/**
 * Count the number of ways to paint an m × n grid with three colors.
 * 
 * @param {number} m - Number of rows
 * @param {number} n - Number of columns
 * @return {number} - Number of ways to paint the grid
 */
function colorTheGrid(m, n) {
  const MOD = 1000000007;
  
  // Generate all valid column states
  const validStates = [];
  const limit = Math.pow(3, m);
  
  for (let state = 0; state < limit; state++) {
    if (isValidState(state, m)) {
      validStates.push(state);
    }
  }
  
  // Precompute valid transitions
  const validTransitions = {};
  for (const state1 of validStates) {
    validTransitions[state1] = [];
    for (const state2 of validStates) {
      if (canTransition(state1, state2, m)) {
        validTransitions[state1].push(state2);
      }
    }
  }
  
  // Initialize DP array
  let dp = new Array(validStates.length).fill(1);
  
  // Fill DP array
  for (let j = 1; j < n; j++) {
    const newDp = new Array(validStates.length).fill(0);
    for (let i = 0; i < validStates.length; i++) {
      const state1 = validStates[i];
      for (const state2 of validTransitions[state1]) {
        const idx = validStates.indexOf(state2);
        newDp[idx] = (newDp[idx] + dp[i]) % MOD;
      }
    }
    dp = newDp;
  }
  
  // Sum up the results
  let result = 0;
  for (let i = 0; i < validStates.length; i++) {
    result = (result + dp[i]) % MOD;
  }
  
  return result;
}
 
/**
 * Check if a column state is valid (no adjacent cells have the same color).
 * 
 * @param {number} state - The column state in base-3
 * @param {number} m - Number of rows
 * @return {boolean} - True if the state is valid, false otherwise
 */
function isValidState(state, m) {
  // Convert state to base-3 representation
  const colors = [];
  let tempState = state;
  
  for (let i = 0; i < m; i++) {
    colors.push(tempState % 3);
    tempState = Math.floor(tempState / 3);
  }
  
  // Check if adjacent cells have different colors
  for (let i = 0; i < m - 1; i++) {
    if (colors[i] === colors[i + 1]) {
      return false;
    }
  }
  
  return true;
}
 
/**
 * Check if two column states can be adjacent (no horizontally adjacent cells have the same color).
 * 
 * @param {number} state1 - The first column state in base-3
 * @param {number} state2 - The second column state in base-3
 * @param {number} m - Number of rows
 * @return {boolean} - True if the states can be adjacent, false otherwise
 */
function canTransition(state1, state2, m) {
  // Convert states to base-3 representation
  const colors1 = [];
  const colors2 = [];
  let tempState1 = state1;
  let tempState2 = state2;
  
  for (let i = 0; i < m; i++) {
    colors1.push(tempState1 % 3);
    colors2.push(tempState2 % 3);
    tempState1 = Math.floor(tempState1 / 3);
    tempState2 = Math.floor(tempState2 / 3);
  }
  
  // Check if horizontally adjacent cells have different colors
  for (let i = 0; i < m; i++) {
    if (colors1[i] === colors2[i]) {
      return false;
    }
  }
  
  return true;
}
 
// Optimized version for larger inputs
function colorTheGridOptimized(m, n) {
  const MOD = 1000000007;
  
  // Generate all valid column states and their color configurations
  const validStates = [];
  const colorConfigs = new Map();
  const limit = Math.pow(3, m);
  
  for (let state = 0; state < limit; state++) {
    if (isValidState(state, m)) {
      validStates.push(state);
      
      // Store the color configuration for this state
      const colors = [];
      let tempState = state;
      for (let i = 0; i < m; i++) {
        colors.push(tempState % 3);
        tempState = Math.floor(tempState / 3);
      }
      colorConfigs.set(state, colors);
    }
  }
  
  // Precompute valid transitions using color configurations
  const validTransitions = {};
  for (const state1 of validStates) {
    validTransitions[state1] = [];
    const colors1 = colorConfigs.get(state1);
    
    for (const state2 of validStates) {
      const colors2 = colorConfigs.get(state2);
      let valid = true;
      
      for (let i = 0; i < m; i++) {
        if (colors1[i] === colors2[i]) {
          valid = false;
          break;
        }
      }
      
      if (valid) {
        validTransitions[state1].push(state2);
      }
    }
  }
  
  // Initialize DP array
  let dp = new Array(validStates.length).fill(1);
  
  // Fill DP array
  for (let j = 1; j < n; j++) {
    const newDp = new Array(validStates.length).fill(0);
    for (let i = 0; i < validStates.length; i++) {
      const state1 = validStates[i];
      for (let k = 0; k < validTransitions[state1].length; k++) {
        const state2 = validTransitions[state1][k];
        const idx = validStates.indexOf(state2);
        newDp[idx] = (newDp[idx] + dp[i]) % MOD;
      }
    }
    dp = newDp;
  }
  
  // Sum up the results
  let result = 0;
  for (let i = 0; i < validStates.length; i++) {
    result = (result + dp[i]) % MOD;
  }
  
  return result;
}
 
// Test cases
console.log(colorTheGrid(1, 1));  // 3
console.log(colorTheGrid(1, 2));  // 6
console.log(colorTheGrid(5, 3));  // 580986